Beat 1/3 cup butter and shortening with an electric mixer on medium to high speed for 30 seconds. Add sugar, baking powder, and salt; beat until combined. Beat in egg, milk, and vanilla. Beat in as much of the 2 cups flour as you can with the mixer. Stir in remaining flour with a wooden spoon. Divide dough in half. If necessary, cover and chill dough for 3 hours or until easy to handle.
Meanwhile, for the cream dough, beat 2 tablespoons butter in a small bowl on medium speed for 30 seconds. Add 2 tablespoons sugar and beat until combined. Beat in half-and-half or light cream. Beat in 1/2 cup all-purpose flour until smooth. Tint brown with paste food coloring.