Coconut Cake with Coconut Cream Frosting

Name: Coconut Cake with Coconut Cream Frosting
Cook time: 3 h
Total time: 3 h
Cuisine: Thai, Asian
Ingredients: Baking spray with flour; 1 cup butter, softened; 2 cups granulated sugar; 1 tablespoon grated lemon zest (from 2 lemons, optional); 1 teaspoon vanilla extract; .5 teaspoon coconut extract; 3 cups bleached cake flour (such as Swans Down); 1 tablespoon baking powder; .5 teaspoon kosher salt; 1 cup whole milk; 6 large egg whites; 6 ounces cream cheese, softened; 2 (16-oz.) pkg. powdered sugar; .25 cup cream of coconut (such as Coco López); 2 teaspoons vanilla extract; .25 teaspoon coconut extract; Leaf green gel food coloring; Super red gel food coloring; Lemon Curd Filling , Cranberry Filling , or Whipped Chocolate Ganache Filling; 1.5 cups unsweetened shredded coconut; 2 Peace Dove Cookies (on lollipop sticks or skewers)