Frosted Cinnamon Buns with Apple Butter

Name: Frosted Cinnamon Buns with Apple Butter
Ingredients: For the cinnamon buns:; 1 cup warm milk; 2½ teaspoons yeast; 4½ cups all-purpose flour; 1 teaspoon salt; ½ cup granulated sugar; 2 eggs, at room temperature; ? cup butter, melted but not hot; 1 teaspoon pure vanilla extract; 1 cup apple butter (homemade or store-bought); 1 cup packed brown sugar; 2 tablespoons ground cinnamon; 1 small apple, cut into small, very thin pieces; For the frosting:; 1 (3 ounce) package cream cheese, softened; ¼ cup butter, softened; 1½ cups powdered confectioner’s sugar; ½ teaspoon vanilla extract