Position racks in the upper and lower thirds of the oven and heat to 375°F (190°C). Line 2 rimmed baking sheets with parchment paper.
In a large mixing bowl, whisk together the tapioca flour, garlic powder, and black pepper until evenly dispersed.
Combine the milk, light olive oil, and sea salt in a small saucepan. Warm over medium heat until the edges are steaming and tiny bubbles appear (no rolling boil), 2 to 3 minutes. Remove from heat.
Pour the hot milk mixture over the tapioca mixture. Stir vigorously with a sturdy spatula until it forms a sticky, shaggy dough. Let it stand 5 minutes to cool slightly and hydrate.
Beat in the eggs one at a time using a hand mixer on medium speed (or a strong arm with a spatula), mixing until smooth and glossy after each addition and scraping the bowl as needed.
Fold in 1 1/4 cups Parmesan and mix for 30 seconds more until the dough is elastic and tacky. Reserve the remaining 2 tablespoons Parmesan for topping.
Transfer the dough to a large piping bag (or a zip-top bag) and snip a 1/2-inch opening; lightly oil the inside of the bag to help the sticky dough move. Pipe tablespoon-size mounds 2 inches apart onto the prepared sheets. Smooth any pointy tips with a damp fingertip and sprinkle each mound with a pinch of the reserved Parmesan.
Bake for 18 to 22 minutes, rotating the pans front to back and top to bottom halfway through, until puffed, set, and deeply golden on the undersides. The puffs should sound hollow when tapped.
Cool 5 minutes on the sheets, then serve warm while the centers are still chewy and the edges crisp.