Using a stand mixer and a large mixing bowl, cream together the softened butter, brown sugar, ground cinnamon, and vanilla. Slowly incorporate the powdered sugar on a low speed. Then add in the milk as the mixer continues on a low speed. Increase the mixer speed to medium and whip for 1 minute until the frosting becomes light and fluffy.
1 cup softened butter, ½ cup brown sugar, 1 teaspoon cinnamon, 1 teaspoon vanilla, 3 cups powdered sugar, 2 tablespoons milk