Position an oven rack in the center of the oven and preheat the oven to 400 F. Line a sheet pan withparchment paper.
Place the tapioca starch in a heat proof bowl. In a saucepan, combine the milk, 4 tablespoons cold water, the oil, and salt. Bring to a boil over medium-high heat. Pour the boiling milk mixture into the tapioca starch and mix until fully incorporated.
Beat in the eggs, one at a time, mixing well until fully incorporated. Mix in the Parmesan, a little at a time, until fully incorporated. Stir in the mozzarella, a little at a time, until fully incorporated. The dough will be very sticky; if it is too sticky to handle, add a little more tapioca starch.
Wet your hands in cold water. Scoop some dough out with a spoon (about 11/2 oz/40 g) and roll the dough between your hands into a ball the size of a golf ball. Place the balls on the lined sheet pan.
Transfer the sheet pan to the oven and bake until the rolls are golden and puffy, about 20 minutes. Serve warm.