Lemon Cake With Lemon Frosting

Name: Lemon Cake With Lemon Frosting
Ingredients: 3 cups sifted all-purpose flour, plus more for dusting; 1 tablespoon baking powder; 3/4 teaspoon salt; 1 cup milk, at room temperature; 2 teaspoons pure vanilla extract; 1 1/2 sticks unsalted butter, softened; 2 cups granulated sugar; 4 large eggs, at room temperature; 2 teaspoons finely grated lemon zest; 1/2 pound unsalted butter, softened; 1 large egg yolk (optional); 1 pound confectioners' sugar; 1/4 cup plus 2 tablespoons heavy cream; 1 teaspoon pure vanilla extract; Pinch of salt; 1 teaspoon finely grated lemon zest; 1 1/2 tablespoons fresh lemon juice