Preheat oven to 375 degrees F.
Combine water, milk, oil, and salt in a small sauce pan and bring to a boil. Meanwhile, put the tapioca starch in a medium bowl. In another bowl grate the cheese and whisk it together with the eggs.
When the milk mixture comes to a boil, pour it over the starch and beat it vigorously with a wooden spoon until you have a cohesive, thick gelatinous paste. Let it cool completely.
When cool, transfer it to the bowl of a stand mixer fitted with the paddle attachment. Add the cheese/egg mixture and beat on medium-high for about 90 seconds until the mixture is smooth. It will be very sticky and stretchy.
Spoon roughly 2-tablespoon-sized quantities (I use a 1 1/2 tablespoon sized small cookie/ice cream scoop to portion) onto 1 to 2 parchment lined-sheet pans and bake 30 to 40 minutes until golden and puffed (if you are using two sheet pans, rotate them from front to back and top to bottom halfway through baking). Eat warm.