Allow cheese to sit out until it is at room temperature. In a large bowl, mix together the cheese, butter and paprika using a pastry blender. Gradually mix in flour, first using the pastry blender, then using your hands. Mix until the dough pulls together. It should form a solid ball with a smooth appearance, but have a crumbly texture when pulled apart. If dough appears too dry, add more shredded cheese.
Preheat the oven to 375 degrees F (190 degrees C). Pinch off a small piece of dough, and cover an olive with it. Roll gently between your palms to smooth and seal the olive inside the ball. Place onto an ungreased cookie sheet and repeat with remaining dough and olives. Place the tray of covered olives into the refrigerator for 10 minutes to firm up.
Bake for 20 to 25 minutes in the preheated oven, or until browned. Serve hot or at room temperature.