Preheat oven to 350°F. Grease two 9-inch round cake pans, line with wax paper; grease paper.
Make banana cake: Using an electric mixer, cream butter and sugar, beating until fluffy, about 5 minutes. Add eggs, one at a time, beating after each addition until well blended. Mix in baking powder, baking soda and salt. Add banana and beat at medium speed until barely incorporated. Mix in milk. Add flour and mix at low speed until smooth. Spoon batter into prepared pans.
Bake cake layers until springy to touch, 35 to 40 minutes. Let cakes cool in pans on a rack for 10 minutes, and then turn out and let cool completely.
Meanwhile, make fudgy frosting: In a medium saucepan, bring cream, sugar and corn syrup to a boil. Reduce heat and simmer, stirring occasionally, for 5 minutes. Remove mixture from heat and add chocolate and butter; stir until completely smooth. Stir in vanilla extract and salt and then pour mixture into a medium bowl set in a larger bowl of ice water. Beat fudge with a handheld electric mixer until it's shiny and thick.
Transfer 1 cake layer to a serving platter. Frost with 3/4 cup fudgy frosting, then top with second layer and spread remaining frosting over top and sides of cake, swirling frosting in a decorative pattern with a knife, if desired.