Preheat the oven to 350 degrees F.
Combine the Cheddar, flours, paprika, onion powder and salt in a food processor. Add the butter and pulse until coarse crumbs form. Add the milk and pulse until the dough forms into a ball.
Form the dough into 1 disk. Cover in plastic wrap and refrigerate for about 30 minutes.
Roll the dough out 1/8-inch thick on a lightly-floured surface using a lightly-floured rolling pin. Form shapes with a cookie cutter, dipping it in flour from time to time to ensure a clean cut. Gently transfer the crackers to a baking sheet lined with parchment paper. Bake the crackers on the middle rack of the oven until they are barely browned at the edges, about 8 minutes.
Remove from the oven and set onto a rack to cool.