Preheat the oven to 350 degrees F. Grease and flour a 9-inch x 13-inch baking dish or pan. Set aside.
Banana Layer
In a medium bowl, mix the melted butter and brown sugar until well combined. Spread the brown sugar mixture evenly over the bottom of the baking dish.
Arrange the sliced bananas in a single layer over the brown sugar. Set the dish aside.
Cake
In a large mixing bowl, beat the butter and sugar until light and fluffy, about 2 minutes. Add eggs one at a time, beating well after each addition. Add the milk and vanilla and beat until combined.
In a medium mixing bowl, stir the cake flour, baking powder, and salt together. Add the dry ingredients to the wet ingredients and mix until just combined.
Pour the cake batter evenly into the pan over the banana slices. (You want to keep moving the bowl as the batter pours in so the bananas don't get pushed away from any one area. This will keep the cake pretty once you remove it from the pan.)
Bake for 30-35 minutes or until the center bounces back when lightly pressed. A toothpick inserted in the center should come out clean, and the middle should be set (no jiggles).
Remove from the oven and cool for 15 minutes in the pan. Then run a knife around the edges of the cake and carefully invert it onto a serving platter. Cut into 12 slices and enjoy!
Notes
If you don't have cake flour available, you can substitute 2 cups of all-purpose flour + 1/4 cup of cornstarch or arrowroot.