The cartoon opens with various shots of famous 1940s celebrities dining or hanging out at The Mocrombo Club—including such personalities as Frank Sinatra (depicted as long and skinny, so much so that he slips into his straw while trying to take a sip from his drink) and Ray Milland (in a parody of The Lost Weekend, where he pays for his drink with a typewriter and receives little typewriters as change). Fudd is a waiter at the Mocrumbo and comes out to find that his next customer is Humphrey Bogart.
Bogart lets Elmer know that he wants fried rabbit, and he wants it within the next 20 minutes—or else! (pulling out a tommy gun). This puts Elmer in a bind, as the restaurant is "fwesh out of wabbit." However, as he is scouring the kitchen, Elmer hears the familiar sound of Bugs munching on some carrots in a corner of the kitchen. Elmer lets Bugs know that Bogart wants to "have" him for dinner. Bugs immediately dresses in a tuxedo and wants to have a peek at what is cooking. Elmer quickly puts a mirror into a pot. Bugs takes a look inside, soon realizes that he himself is the main course, and makes a quick getaway.
Bugs eventually manages to get out of the kitchen, dressing like Groucho Marx in an attempt to fool Elmer—but Elmer is dressed as Harpo. Bugs tries to make a getaway, but is stopped by the large stomach of Sydney Greenstreet. He runs into Carmen Miranda's dressing room and hides in her famous fruit hat. Carmen then does a song and as she walks off the stage, Elmer starts chasing Bugs. Elmer runs away from the audience leaving Bugs to dance to the same song Carmen did.
Bugs then makes his way back to the kitchen, where he enjoys the audience loving his performance. He saw Elmer approaching, so he then pretends to be a pie chef and continues splattering Elmer in the face. On the third pie which was a coconut custard pie with whipped cream, Elmer realizes that Bugs is the pie chef, so he threw that last at Bugs. When Bugs manages to duck that pie, it hits Bogart in the face. Bogart grabs Elmer and asks him, "Why did you hit me in the face with a coconut custard pie with whipped cream?" Bogart then warns Elmer that he has just 5 minutes to come up with his fried rabbit. Elmer searches frantically, but cannot find one in time. Bogart comes in, and Elmer thinks he's about to die. Bogart sticks his hand in his jacket, only to pull out a handkerchief and dab his forehead as he resigns, "Baby will just have to have a ham sandwich instead." Upon hearing of "Baby", Bugs jumps out of his hiding place which was the clock that told Elmer his time was up (it was assumed that Bugs himself tampered with the clock) and takes his place as the main course (Lauren Bacall being "Baby"), noting, "Remember, garçon, the customer is always right! If it's rabbit Baby wants, rabbit Baby gets!", before howling and at Bacall.