Preheat oven to 350°F (175°C). Line a 9"x 13"x 2" baking pan with parchment paper. Grease (or butter and flour) the paper.**
Whisk together the flour, baking powder, baking soda, and salt. Set aside.
Using an electric mixer on medium speed, beat the butter and sugar until light and fluffy. Add the eggs, one at a time, mixing well after each addition. Mix in the vanilla.
Reduce mixer speed to low. Add the flour mixture in 3 portions, alternating with 2 portions of coconut milk. Mix just until combined.
Transfer the batter to the prepared pan and spread evenly. Tap the pan on the counter a few times to get rid of large air pockets.
Bake 35 to 40 minutes, or the cake is golden brown and a pick inserted into the center comes out clean.
Cool the cake completely in the pan on a wire rack.
To make the frosting:
Beat the cream cheese and dulce de leche until well-blended. Mix in the vanilla, beating until combined.
Spread the frosting on the cooled cake. Garnish with toasted coconut flakes.