Cream butter with electric beaters until soft and light, 1-2 minutes.
Add maple syrup, salt, and vanilla. Blend well.
Sift in flour and cornstarch. Add candy cap sugar. Beat ingredients on low just until the dough starts to come together. Turn dough out onto a flat work surface covered with parchment. Roll dough in between 2 pieces of parchment paper (don't add flour, it will make the cookies tough!) until fairly thin, about 1/4 inch.
Chill dough for at least 20 minutes to firm up, then cut dough into desired shapes using cookie cutters, a sharp knife, or a biscuit cutter.
Chill again for at least 20 minutes before baking. While cookies are chilling, preheat oven to 325° F and line 2 baking sheets with parchment paper.
Bake cookies until firm but not yet browning, about 12-15 minutes. Time may vary depending on the size of your cookies.
Allow to cool slightly, then sprinkle liberally with additional candy cap sugar.