Place Cheddar cheese, flour, and butter in a food processor. Blend until cheese is finely ground and a crumbly dough forms.
Wrap each olive with a piece of the cheesy dough, covering the olive completely. Place olive balls on a cookie sheet and freeze for 1 hour.
Preheat the oven to 400 degrees F (200 degrees C). Spread frozen olive balls on a baking sheet.
Bake in the preheated oven until lightly browned, 15 to 20 minutes. Let cool for 5 minutes before serving. Eat with caution as olives will still be hot.
