Preheat the oven to 350 degrees. In a stand mixer with a paddle attachment, beat butter and shortening together for 30 seconds on medium-low speed until completely combined.
Add sugar, vanilla, and salt and beat for another minute. Once combined, add flour and mix on low until it comes together to form a crumbly dough. You want it to hold together when pressed, but not to form a sticky ball on its own. If the dough is too sticky, add a tablespoon of flour. If it's too dry, add a tablespoon of water.
Dump the dough onto a large sheet of parchment paper and cover with another sheet. Using a rolling pin, roll out the dough until it is 1/2 inch thick. Place the dough (still between the parchment) on a large cookie sheet and chill in the refrigerator for 30-60 minutes.
Once chilled, cut out your shapes with cookie cutters or a pizza roller (I prefer the pizza roller because it's fast and easy) and place on a parchment-lined cookie sheet. Sprinkle the top of the cookies with coarse sugar and bake for 18-20 minutes, or until very lightly golden around the edges.