Homemade Boston Cream Pie

Name: Homemade Boston Cream Pie
Prep time: 25 min
Cook time: 20 min
Total time: 45 min
Cuisine: American
Ingredients: 1/3 cup sugar; 3 tablespoons cornstarch; 1-1/2 cups whole milk; 2 large egg yolks; 1 tablespoon butter; 1 teaspoon vanilla extract; 1 cup sugar; 1/3 cup shortening; 2 large eggs, room temperature; 1 teaspoon vanilla extract; 1-1/4 cups all-purpose flour; 1-1/2 teaspoons baking powder; 1/4 teaspoon salt; 3/4 cup whole milk; 3 tablespoons water; 2 tablespoons butter; 3 tablespoons baking cocoa; 1 cup confectioners' sugar; 1/2 teaspoon vanilla extract