Preheat oven to 375 degrees F (190 degrees C).

Put Cheddar-Monterey Jack cheese in a bowl; add butter. Cover bowl and let sit until warmed to room temperature.

Combine flour and paprika together in a separate bowl.

Mix cheese and butter together using your hands. Slowly add flour mixture to cheese-butter mixture until dough holds together in a ball. Roll dough onto a work surface, about 1/8-inch thick. Cut dough into cracker shapes using cookie cutters or a knife; sprinkle salt over dough. Arrange dough pieces on a baking sheet.