Coconut Cake

Name: Coconut Cake
Cuisine: American
Ingredients: Butter and flour for the pans; ¼ pound unsalted butter; 4 eggs, separated; 2 cups all-purpose flour; 1 tablespoon plus 1 teaspoon baking powder; ½ teaspoon salt; ⅓ cup fresh or canned coconut milk; ⅓ cup fresh or canned coconut milk; Grated zest of 1 lemon; ⅓ cup fresh lemon juice; 1½ tablespoons cornstarch; 8 egg yolks, at room temperature; 2 tablespoons butter; 1½ cups sugar; 2 eggs whites, at room temperature; ¼ teaspoon cream of tartar; ¼ cup ice water; 1 cup shredded unsweetened coconut, to dust the cake