Directions for the cookie dough:
Preheat oven to 350 degrees. Combine the shortening and sugar in the bowl of an electric mixer (or a large bowl with a hand blender will do) and beat until light and fluffy. Add egg and beat to combine. Add vanilla and milk and beat to combine. In a separate bowl, sift together the flour, salt, and baking powder. Add to the wet ingredients and mix to combine. Turn dough out onto a piece of plastic wrap or waxed paper. Wrap tightly and refrigerate for one hour. Roll out on a lightly floured surface approximately 1/2 inches thick. Cut into desired shapes and place on baking sheets. Bake for 9 minutes, or until edges are just golden brown. Let cool on the pan for 5 minutes and then move to wire racks to cool completely before frosting and decorating.
Directions for the frosting:
Beat together the sugar and butter until smooth. Add the vanilla and milk and beat to combine. Add more milk, 1 T. at a time, if needed to reach desired spreading consistency. Add desired food coloring and mix thoroughly (you can separate into smaller bowls to make smaller batches of various colors. I usually let my daughter choose the colors for her batch).
Note: I like to make the frosting as the cookies cool, but you can also make it ahead, refrigerate, and then bring to room temperature before spreading.