In a large mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add 2 cups of the powdered sugar, the milk, and vanilla. Beat until smooth. Add remaining powdered sugar and beat until combined. Beat on high speed for 2 minutes. Place frosting in a pastry bag fitted with a large star tip or in a zip-top bag with one corner cut; set aside.
Remove paper bake cups from cupcakes, if using. Cut cupcakes in half horizontally. Place bottom half of cupcakes, cut side up, in half-pint canning jars. Pipe frosting on top of each. Add cupcake tops, cut sides down. Pipe frosting on top of each. Add lids to jars and decorate as desired.