Position a rack in the center of your oven and preheat to 325 degrees. Line an 8-inch square baking pan with a piece of parchment paper and set aside.

In a large mixing bowl, whisk together the oil, water, egg yolks, and vanilla, then whisk in 1/2 cup sugar. Place a fine-mesh strainer over the bowl and sift in the flours and baking powder. Whisk until completely smooth.

In the clean, dry bowl of a stand mixer fitted with the whip attachment, whip the egg whites with the cream of tartar on medium-high speed until soft peaks form. Slowly add in the remaining 2 Tbsp sugar and whip until the whites are glossy and just hold a firm peak, one to three minutes.

Using a flexible silicon spatula, fold 1/3 of the whites into the batter, then gently fold in the remaining whites until just combined and no streaks remain. Immediately pour batter into prepared pan. Place in the oven and bake for 40 - 50 minutes or until a toothpick comes out of the center clean. Remove from rack and let cool in the pan completely.

To make the milk mixture: Place sugar, vanilla bean seeds, and coconut milk in a medium saucepan. Bring to a bare simmer over medium heat, stirring frequently, then remove from heat. Cove and let steep for 10-20 minutes to infuse the vanilla.

Once the cake has cooled, using a biscuit cutter, cut it into 9 circles. Leaving it in the pan, poke all over with a toothpick and pour 1 1/2 cups of the coconut milk mixture over the cake, letting it absorb the milk. Use a small offset spatula to pry the cake rounds and peel away any scraps (which can be saved for snacking!), placing the cake rounds onto a baking sheet lined with parchment paper. Cover the cakes loosely with plastic wrap and let chill for at least one hour (also cover the remaining milk mixture and stick in the fridge as well).

To finish, preheat oven to 325 degrees. Spread coconut flakes on a small baking sheet and toast until golden, 5-10 minutes.

Serve cake rounds in shallow bowls topped with coconut, mango chunks, and lime zest.