Whisk flour, baking powder, and salt in a medium bowl. In a large bowl, beat egg yolks, ½ cup sugar, coconut milk, melted butter, vanilla, and coconut extract until smooth, about 1 minute.

In a clean bowl, beat egg whites and cream of tartar until foamy. Gradually add remaining ½ cup sugar, then whip on high until stiff, glossy peaks form, 3 to 4 minutes.

Stir flour mixture into yolk mixture until almost combined. Fold in the whipped whites with a spatula until no white streaks remain, about 30 seconds.

Preheat oven to 350°F (180°C). Grease and line two 8-inch round pans. Divide batter evenly, tap pans, and bake 25 to 30 minutes until a toothpick comes out clean. Cool 10 minutes in pans, then turn out to cool completely.

Whip heavy cream, powdered sugar, and coconut milk powder to medium peaks, 2 to 3 minutes. Frost the cooled cake layers, scatter shredded coconut on top, slice, and serve.