Preheat oven to 375degrees F (190 degrees C).
Pour olive oil, water, milk, and salt into a large saucepan, and place over high heat. When the mixture comes to a boil, remove from heat immediately, and stir in tapioca flour and garlic until smooth. Set aside to rest for 10 to 15 minutes.
Stir the cheese and egg into the tapioca mixture until well combined, the mixture will be chunky like cottage cheese. Drop rounded, 1/4 cup-sized balls of the mixture onto an ungreased baking sheet.
Bake in preheated oven until the tops are lightly browned, 15 to 20 minutes.
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