Make the topping:
Preheat the oven to 350ºF. Grease a 9-inch round nonstick pan and dust with flour.
Heat the butter in a medium saucepan over medium heat until foaming. Whisk in the brown sugar, turn the heat to low, and cook, whisking, for 2 minutes. Scrape the mixture into the prepared pan and smooth with a spatula. Arrange the banana slices in concentric circles on top of the sugar mixture. Set aside.
Make the cake
Combine the flour, cocoa powder, baking soda, and salt in a medium mixing bowl.
Combine the butter and granulated sugar in a large mixing bowl and cream with an electric mixer on medium-high speed until fluffy, about 3 minutes.
With the mixer on low speed, add the eggs, one at a time, scraping down the sides after each. Turn the mixer to high speed and beat until the mixture is light and increased in volume, about 2 minutes. Stir in the vanilla.
With the mixer on low, stir in 1⁄3 of the flour mixture. Stir in 1⁄2 of the buttermilk. Repeat with the remaining flour and milk, ending with the flour. Scrape down the sides of the bowl and beat the batter on high speed for 30 seconds.
Pour the batter over the bananas, gently spreading it into an even layer.
Bake until a toothpick inserted into the center comes out clean, 40 to 45 minutes. Transfer the pan to a wire rack and let stand for 5 minutes. Holding the pan and a plate together with oven mitts, immediately invert the hot cake onto the plate. If necessary, replace any fruit stuck to the bottom of the pan. Let the cake cool for 20 minutes and serve warm, or serve at room temperature.
Store uneaten cake in a cake keeper, or wrap in plastic and store at room temperature for up to 2 days.