Combine milk, water, oil, and salt in a saucepan over medium-high heat. Bring to a full rolling boil, about 3-4 minutes.
0.5 cup milk, 0.25 cup water, 0.25 cup oil, 1 tsp salt
Pour the boiling liquid immediately over the tapioca flour in a large mixing bowl. Stir vigorously with a wooden spoon for 2-3 minutes until dough forms and no dry flour remains.
2 cups tapioca flour
Let dough rest 10 minutes at room temperature, stirring occasionally to release steam. Dough should be warm but not hot (around 120-130°F).
Add eggs one at a time, stirring after each addition until smooth. Then add grated Parmesan and mix 1-2 minutes until completely incorporated and uniform with no lumps.
2 large eggs, 1 cup Parmesan cheese
Preheat oven to 375°F. Use a 1.5 tablespoon ice cream scoop to portion dough onto a parchment-lined baking sheet, spacing balls 2 inches apart. Wet hands lightly if dough sticks.
Bake 20-25 minutes on the lower oven rack until rolls puff, become lightly golden, and feel firm to touch. Let cool on a wire rack 10 minutes before serving.
