Combine the milk, oil, and salt in the saucepan, and whisking occasionally, bring it to a gentle boil over medium heat. Remove from heat as soon as you see big bubbles coming through the milk.
Add all of the tapioca flour to the saucepan and stir until you see no more dry tapioca flour. The dough will be grainy and gelatinous at this point.
Transfer the dough to the bowl of a standing mixer fitted with a paddle attachment. (Alternatively, you can do the next few steps by hand. Be prepared for a work-out.) 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.
Whisk the eggs together in a small bowl. With the mixer on medium, beat the eggs into the dough in two additions. Wait until the first addition has been fully incorporated into the dough before adding the second. Scrape down the sides of the bowl as needed.
With the mixer on medium, beat in the cheese until fully incorporated. The resulting dough will be very sticky, stretchy, and soft with a consistency between cake batter and cookie dough.
Using an ice cream scoop, a tablespoon measure, or a dinner spoon, scoop rounded portions of the dough into mounds on the parchment-lined baking sheet. Space the mounds an inch or two apart. Dip your scoop in water or spray with cooking spray to prevent sticking.
Transfer the sheet with the puffs to the oven and bake for 25-28 minutes, until the puffs have puffed, the outsides are dry, and they are JUST starting to colour. Do not over bake! Cool briefly and eat.