Preheat oven to 375 degrees F (190 degrees C). Zest and juice the Lime (1) and reserve half of the juice. Peel and slice the Mango (3 cup). Toss mangoes in lime juice in a medium bowl.
Melt Unsalted Butter (1/4 cup) and pour into the bottom of a springform pan. Sprinkle Brown Sugar (1/3 cup) evenly over the bottom of the pan. Arrange the mangoes in a sunshine pattern along the bottom of the pan, overlapping as you go.
In a food processor, add All-Purpose Flour (3/4 cup), Cornmeal (1/2 cup), Granulated Sugar (1/3 cup), Baking Powder (2 teaspoon) and Salt (1/4 teaspoon). Pulse to combine. Cut Unsalted Butter (1/4 cup) into chunks and add to flour mixture.
Pulse until mixture resembles coarse meal. In a large bowl, whisk together Egg (1) and Milk (3/4 cup). Add flour mixture and lime zest. Whisk until just combined. Pour batter evenly over mangoes, and bake until golden, 45-50 minutes.
Remove from oven, and cool for 15 minutes. Run a sharp paring knife around the edges to loosen the cake. Remove the collar from the pan. Set a cake plate on top of the cake, and quickly invert the cake onto the plate. Remove pan bottom.
Just before serving, pour Powdered Confectioners Sugar (1/3 cup) into a fine sieve, and tap the side of the sieve with your hand to sprinkle sugar over the cake. Enjoy!