Big Tasty is Barry's famous catchphrase that has been in the Goldbergs many times and has also been referenced too. In S01E02 Daddy Daughter Day, when Barry is asking Murray for $20, Murray says no, but Barry says its for Big Tasty and Murray shouts at his middle son saying that "Who the hell is Big Tasty?" And Barry says it's his rap thing. It is done again in a clip at the end where Barry is rapping a rap he invented to Pops, in the last line Barry says "when I say big, you say tasty, big-" and Pops asks what's going on? And Murray shouts/replies that Barry is a moron and to stop doing what he's doing.
In S01E19 The President's Fitness Test, When Barry is singing a French rap to impress a French woman, in the raps subtitles it has 'Big Tasty' in, which in French its 'Grand Savourex.'
In S02E15 Happy Mom, Happy Life, when Erica is the new leader of the JTP (when the JTP previously kicked Barry out) they call Erica 'Big E' to which Barry complains its way to close to his name 'Big Tasty', which will make people confused.
In S03E20 Dungeons and Dragons, Anyone?, Barry creates a Dungeons and Dragons character called 'Lord Big of Tasty'.
In S04E14 The Spencer's Gift, when Barry gets a Job at Spencer's Gift, on his shirt, there is a label saying 'B. Tasty' a reference to 'Big Tasty'.
In S04E17 Deadheads Barry says Big Tasty whilst standing on the table.