In a large mixing bowl, combine the grated cheese and tapioca flour.
In a separate bowl, whisk together the milk, sugar, baking powder, salt, egg, and melted butter.
Gradually add the wet ingredients to the dry ingredients, mixing until a smooth dough forms. The dough should be slightly sticky but manageable. If too dry, add a little more milk.
Take small portions of dough and roll them into 1-inch balls.
Place the formed balls on a parchment-lined tray or plate.
Heat vegetable oil in a deep fryer or large skillet over medium heat. The oil should be about 2-3 inches deep and reach 350°F (175°C).
Carefully drop a few dough balls into the hot oil, being careful not to overcrowd the pan. Fry in batches if necessary.
Fry the buñuelos, turning them occasionally, until they are golden brown and puffed up, about 4-6 minutes.
Remove the buñuelos with a slotted spoon and drain them on paper towels.
Enjoy your meal!