Preheat oven to 450°F. Line 2 baking sheets with parchment paper.

Place milk, oil, and salt in a medium saucepan; bring to a gentle boil over medium heat, stirring occasionally. Remove from heat when you see big bubbles coming to the surface.

Add all of the tapioca flour and stir with a wooden spoon until you see no more dry tapioca flour. The dough will be grainy and gelatinous at this point.

Transfer the dough to a large bowl. Beat the dough for a few minutes at medium speed until it smooths out and has cooled enough that you can hold your finger against the dough for several seconds. With the mixer on medium speed, beat the eggs into the dough one at a time, waiting until the first egg is fully incorporated before adding the second. Scrape down the sides of the bowl as needed.

Beat in the cheese on medium speed until fully incorporated. The resulting dough will be very sticky, stretchy, and soft. It will not be completely smooth. You may need to add additional tapioca flour at this time to achieve the right consistency.

Have a small bowl of water ready, dip the scoop into the water if necessary, then dough, by level tablespoons onto the baking sheets, spacing them about 1 1/2-inches apart (24 per baking sheet). For larger puffs, scoop the dough with a small (1 ounce or 2 tablespoon) ice cream scoop, spacing them about 2-inches apart (12 per baking sheet). Dip your scoop in water between scoops to prevent sticking. You can also roll the puffs between your palms, rolling them into the size of golf balls, wet hands often to prevent sticking.

Place the baking sheets in the oven and immediately reduce the heat to 350°F. Bake for 15 minutes. Rotate the baking sheets between racks and from front to back. Bake until the puffs have puffed, the outsides are dry, and they are just starting to turn golden-brown on the bottoms, 10 to 15 minutes more.

Cool for a few minutes and eat warm.