Beat butter with an electric mixer on medium to high speed for 30 seconds. Add the 1/2 cup sugar, vanilla, and 1/4 teaspoon salt; beat until combined, scraping sides of bowl occasionally. Beat in egg yolk. Beat in as much of the flour as you can with the mixer. Stir in remaining flour with a wooden spoon.
Shape dough into 1-inch balls. Roll balls in the 1/4 cup sugar; place 2 inches apart on an ungreased cookie sheet. Flatten until about 1/4 inch thick. Bake in a 350 degree F oven for 8 to 10 minutes or until bottoms are lightly browned. Remove from oven. Transfer to wire racks and cool for 2 minutes. Press a peanut butter cup half, cut side down, into each cookie; cool completely.
To decorate, tint portions of frosting desired colors with food coloring. Pipe a basket handle, flowers, and leaves above candy basket as desired. Makes about 48 cookies.