In a large mixing bowl stir together flour, pudding mix, and baking powder; add the 1/2 cup milk, butter, and egg. Beat with an electric mixer on medium speed for 2 minutes.
Grease the bottom and sides of an 8-inch springform pan; place on a baking sheet. Pour the batter into the prepared pan. Slice the 2 bananas; arrange slices atop batter. Set aside.
In a medium mixing bowl beat cream cheese, sugar, the 2 Tbsp. milk, lime juice, and rum extract on medium speed till smooth. Spoon cream cheese mixture over bananas, carefully spreading mixture to cover.
Bake in a preheated 350-degree oven for 30 to 35 minutes or till center is set. Cool in pan for 15 minutes on a wire rack. Loosen crust from sides of pan. Cool for 30 minutes more. Cover and chill at least 2 hours before serving.
To serve, remove sides of springform pan; garnish cake with additional banana slices and lime peel strips.