Preheat the oven to 375.
Beat together the shortening, butter, and 1 and 1/2 cups white sugar until light and creamy. (Do not melt or soften your butter.)Beat in the egg, egg yolk, corn syrup, and vanilla extract. Beat in the peppermint extract to taste. (I like less extract and more actual peppermint so I only add 1/4 tsp. Add 1/2 tsp for a stronger flavor)
Add in the flour, baking powder, salt and peppermint crunch. Mix until just combined.
Shape into thick, flat discs (see picture).
In a small bowl toss together the remaining 1/2 cup white sugar with the coarse sparkling sugar (or just use the white sugar).
Roll the cookie balls in the sugar to coat.
Bake 2 inches apart on a parchment lined cookie sheet.
Bake 9-12 minutes.
The key to soft sugar cookies is slightly under-baking the cookies, letting them cool most of the way, and then spacing them in a bag (sealing the bag) when they are still a little warm. This keeps your cookies ultra soft!