Heat the butter and milk in a large (4 qt) saucepan over medium until it starts to boil.
Remove from the heat and add the tapioca flour, stirring vigorously to mix. This is a lumpy, sticky dough that will remind you of making cream puff dough throughout this recipe. Let this rest, in the saucepan, with periodic mixing, for 20 minutes.
Add the cheeses and blend as best you can.
Add the yeast and eggs. Stir to blend, and then knead with your hands for 5-10 minutes. There will still be small lumps of cheese, which is fine.
Roll into a ball and divide into quarters. Each quarter will make 6 rolls, so now divide each quarter in half and roll out in your hands and break into 3 parts. Place these into a 24-well mini-muffin pan. The amount of dough will more or less fill the cavity. If you have a good non-stick muffin tin, you do not need to pre-grease it.
Preheat the oven to 450F. Place the muffin tin into the oven and lower the temperature to 350F. Bake for about 20 minutes until the tops are golden brown and stiff. Remove from the oven and cool on a rack. The outside should be crisp and the inside should be sticky and a bit gooey.