Lightly grease or spray two mini muffin pans (24 cavities total).
Bring butter, water, milk, and salt to a boil in a saucepan. While heating, measure tapioca flour into a bowl.
Once wet mixture is reaches boiling, remove from the heat and pour over tapioca flour. Beat with an electric mixer until elastic.
Add garlic and cheese and beat until just incorporated.
Make sure the dough is cool before proceeding. If the mixture is too hot from the boiled liquids, it will scramble the eggs. Lukewarm is ok, but not hot to the touch. (Feel a couple areas to make sure there aren't hot pockets). Then add the eggs and beat until combined.
Fill muffin cups ¾ full with mixture. Bake 20 mins until speckled.