Combine 1 large egg, ¼ cup (2 oz) of the buttermilk, 1 teaspoon vanilla extract and finely grated zest from 1 lime in a small bowl.
Sift together 6 ¾ oz cake flour, 1 ½ teaspoons baking powder and ¼ teaspoon table salt in a mixing bowl, add 8 oz granulated sugar and 2 oz almond flour. Run the mixer on low speed for 30 seconds to combine the dry ingredients.
Add 4 oz butter to the dry ingredients and mix until combined. Add the remaining ¼ cup of buttermilk to the flour and butter mixture. Turn the mixer to medium high for 2-3 minutes.
Turn off the mixer and scrape the bowl and paddle. Add the egg mixture in two batches, scraping between additions.
Starting from the outer edge of the pan, gently dollop the batter over the mango slices. Spread the batter to an even layer.
Bake until the center of the cake springs back lightly when pressed, or a toothpick inserted in the center comes out clean, about 30 minutes. Cool in the pan for 15 minutes.
Unmold the cake while it's still a little warm by running a paring knife around the sides of the cake and inverting onto a serving platter. If any caramel or mango slices stick in the pan scrape them out with a small spatula and replace on the cake while still warm.
Serve warm or room temperature.