Preheat the oven to 375°F. Lightly grease a couple of baking sheets; or line with parchment.

Put the butter, water, milk, and salt in a saucepan, and heat until the butter has melted and the mixture has come to a full boil. While the mixture is heating, put 2 cups of tapioca flour into a mixing bowl.

Pour the boiling butter mixture over the tapioca flour, beating to combine. Beat at high speed until the mixture becomes smooth and elastic-looking; this will happen very quickly.

Beat the garlic and cheese into the dough until well combined.

Stick your finger into the dough. If it's uncomfortably hot, let it sit for a couple of minutes to cool a bit; you don't want to cook the eggs when you beat them in. If it seems hot but not burning hot, continue with the next step.

With the mixer going, gradually dribble in the beaten eggs, beating until well combined and smooth. If your batter is thick but pourable, like cake or pancake batter, beat in additional tapioca flour/starch until it's thick enough to hold its shape when you scoop some onto a baking sheet.

Drop the mixture in 2-tablespoon balls (about the size of a golf ball) onto the prepared baking sheets, spacing them about 1 ½" apart.

Bake the buns for about 20 minutes, until they have a freckled appearance (from the browning cheese), and they're beginning to color a bit. Remove them from the oven, and serve hot.

Wrap any leftovers in plastic. Store at room temperature for a couple of days; freeze for longer storage. Rewarm briefly before serving.