Preheat oven to 350°.
Melt 1 tablespoon butter in a large nonstick skillet over medium-high heat. Add apple; cook 5 minutes or until tender.
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, and salt in a bowl, stirring with a whisk. Combine 1/4 cup butter, granulated sugar, cream cheese, 1 teaspoon vanilla, and almond extract in a large bowl; beat with a mixer at medium speed until blended.
Combine milk, egg, and egg white. Add flour mixture and milk mixture alternately to cream cheese mixture, beginning and ending with flour mixture. Stir in apple. Pour batter into a 9-inch round cake pan coated with cooking spray. Sprinkle with almonds.
Bake at 350° for 55 minutes or until a wooden pick inserted in center comes out clean. Cool in pan 10 minutes on a wire rack; remove from pan.
Combine 1/4 teaspoon vanilla, powdered sugar, and water in a small bowl. Drizzle over cake. Serve cake warm or at room temperature.