1. Preheat an oven to 450 degrees F (230 degrees C).
2. Combine the canola oil, water, and salt in a saucepan and bring to a boil. Place the tapioca starch in a metal bowl; pour the oil and water mixture over the tapioca; mix thoroughly. Beat in the egg. Stir in the yogurt, Parmesan cheese, and mozzarella cheese. Pour the mixture into mini-muffin tins.
3. Place on middle rack of the preheated oven. Reduce heat to 350 degrees F (175 degrees C). Bake until slightly golden, 25 to 30 minutes.