Sheldon cannot find the perfect wedding date and begins talking in his sleep, adopting the persona of a laid-back person who goes with the flow. Amy and Penny believe that his subconscious mind is trying to tell him to be more relaxed; his attempt to be so while wearing flip-flops ends in disaster. He decides to leave all the wedding planning to Amy while he wears a Star Trek uniform underneath his tuxedo. Meanwhile, Raj and Stuart both become interested in Bernadette's new coworker Ruchi. While she likes them both as friends, she does not want a relationship with anyone.
“I was there the moment when Leonard and Penny met. He said to me that their babies would be smart and beautiful. And now that they’re expecting, I have no doubt that that will be the case,” Sheldon says, accidentally revealing the baby news even before Penny’s parents know. “I apologize if I haven’t been the friend that you deserve. But I want you to know, in my way, I love you all.”
Howard and Bernadette learn their second child will be a boy, leading Howard to doubt whether he can be a good father to a son. He and Sheldon go out in the desert to test launch a model rocket, but it explodes, causing him further doubt. On the way home, Howard does a good job coaching Sheldon to drive them home, for which Sheldon tells him he will be a good teacher to his son. Leonard's mother Beverly begins talking to Penny as a friend and confidant, troubling Leonard, especially when he learns that Beverly told Penny that she was proud of her, a level of praise she never bestowed upon Leonard himself. When Leonard confronts Beverly, he is touched when she says that of all of her children's spouses, Penny is the one by whom she is most impressed and that, for this, she is indeed proud of him. Meanwhile, Raj helps Bernadette turn baby girl clothes into boy ones.
According to Steve Holland who is the show-runner starting with this season, Wil Wheaton will return in this season since his absence from Season 10. And this has confirmed to be true since it has been stated that he reappeared in "The Proton Regeneration" (S11E6), along with Professor Proton, their first appearances since "The Opening Night Excitation" (S9E11) and "The Celebration Experimentation", respectively and a span of 43 episodes and a span of 37 episodes, respectively. Wil also returned in the 15th episode. Wil will also return for Sheldon and Amy's Wedding.
Like the previous three seasons, the first five episodes aired on Mondays due to CBS' contractual rights to air the Thursday Night Football games. After Thursday Night Football ended, the series returned to a Thursday schedule starting on November 2, 2017. Filming for the eleventh season began on August 15, 2017; it was also announced with the taping report that the premiere for the eleventh season would be titled "The Proposal Proposal". Before the season premiered, five episodes were filmed from August 15 to September 19, 2017.
Sheldon and Amy's wedding day arrives, with many friends and family attending, including Amy's domineering mother (Kathy Bates) and quiet father (Teller); Sheldon's mother Mary, brother George, and sister Missy, who is pregnant with her second child and separated from her husband; and Mark Hamill, who replaces Wil Wheaton as officiant as a favor to Howard who returned his lost dog. Sheldon cannot get his bow-tie to be symmetrical and conversations with Amy and his mother give him an epiphany about superasymmetry. Sheldon and Amy, along with Leonard, get caught up figuring out the math of the theory during the wedding ceremony, making Hamill take Star Wars questions to stall for time. Penny retrieves the couple, who then decide that they have the rest of their lives to make science together. Amy and Sheldon then express their vows. Amy recites a set of heartfelt vows, leaving Sheldon initially at a loss for words, before he reciprocates her loving words. They are pronounced as husband and wife.
After learning Sheldon went behind their backs to work with the military again, Leonard and Howard say Sheldon is like Thomas Edison, taking credit for others' ideas, while they are more like Nikola Tesla. Leonard and Howard bring in Barry Kripke to help create a better idea than Sheldon's, but Kripke goes to the military himself, cutting all three of them out. Meanwhile, Bernadette fears Ruchi is trying to steal her projects at work while she is on maternity leave and enlists Raj to spy on her. Though he finds proof that Ruchi may be stealing from Bernadette, Raj tries to defend Ruchi like a boyfriend would, pointing out Bernadette's hypocrisy as she would most likely have stolen from other people's projects as well. Ruchi is not happy about this and promptly dumps Raj.
Mayim Bialik as Amy Farrah Fowler (guest star season 3, starring seasons 4–12): A woman selected by an online dating site as Sheldon's perfect mate. Amy is from Glendale, CA. While she and Sheldon initially share social cluelessness, after befriending Penny and Bernadette she eventually becomes more interested in social and romantic interaction. Her relationship with Sheldon slowly progresses to the point at which Sheldon considers her his girlfriend, eventually they get married. Amy believes she and Penny are best friends, a sentiment that Penny does not initially share. Amy has a Ph.D. in neurobiology.
Sheldon needs half a billion dollars to prove his latest concept of string theory, which the University cannot afford to fund. Crowdfunding and selling some of his most valuable comic books to Stuart give him a small start. When Raj mentions gambling in Las Vegas, Sheldon goes there but is caught calculating odds by security before he can make any bets. Meanwhile, Amy takes Penny and Bernadette shopping for her wedding dress. She loves an old-fashioned one that the other girls admit that they find ugly, though Penny assures Amy she can make her own decisions about her wedding. Sheldon, however, comes home and sees Amy in the dress and loves how she looks.