In a large mixing bowl, combine tapioca starch, salt, baking powder, milk, butter, and eggs. Using your hands, knead dough until thoroughly combined, about 2 minutes.
Add chopped cheddar and Grana Padano to the dough. Knead gently to evenly distribute the cheeses while allowing some larger chunks of cheese to remain, about 2 minutes.
Cover the tapioca dough with plastic wrap pressed directly onto the dough's surface. Refrigerate overnight to allow the starch to fully hydrate.
Preheat the oven to 375°F (190°C) and adjust oven rack to the center position. Remove tapioca dough from refrigerator and roll into 2-inch balls using the palms of your hands. Make an indentation in the bottom of each roll using the back of a wooden spoon or your thumb.
On a parchment-lined rimmed baking sheet, arrange the rolls leaving 1 inch of space between them. Bake until puffed and golden brown, about 20 minutes, rotating the pan once during baking.
