Stir together olive oil, water, milk, and salt in a large saucepan over high heat. When the mixture comes to a boil remove from heat and immediately stir in tapioca flour and garlic until smooth. Set aside to rest for 10 to 15 minutes.
Stir the cheese and egg into the dough mixture until combined (consistency will be chunky like cottage cheese). Drop rounded, 1/4 cup-sized balls of dough onto an ungreased baking sheet.
Bake until lightly browned, 15 to 20 minutes. Cool on wire racks.