Step 1Heat the oven to 350 degrees.
Step 2In the bowl of a stand mixer, or in a large bowl using an electric mixer, cream together the butter and one-half cup powdered sugar until light and smooth, 2 to 3 minutes. Beat in 1 teaspoon vanilla, and then the salt. Stir in the flour, a little at a time, until thoroughly mixed and smooth to form the dough.
Step 3Gather the dough and roll it to a thickness of one-fourth inch on a floured surface. Cut out cookie shapes from the dough.
Step 4Space the cookies about 1 inch apart on an ungreased cookie sheet and bake until just browned on the bottom but still light on top, about 10 minutes. Cool briefly on the pan, and then transfer to a cooling rack to cool completely.
Step 5Make the glaze: In a medium bowl, stir together the remaining powdered sugar and vanilla extract with just enough water to reach the desired consistency. To color the glaze, divide the dough and tint with food coloring as desired.
Step 6Ice the cookies as desired.