Preheat the oven to 425 degrees F. Line a baking sheet with parchment.
Put the tapioca flour in the bowl of a stand mixer fitted with the paddle attachment.
Combine the milk, oil, salt and 1/2 cup water in a medium saucepan and bring to a boil while whisking. Remove from the heat and pour over the tapioca flour in the mixing bowl. Begin to mix, first starting on low, then gradually increasing the speed to high as the mixture begins to thicken and turn smooth. (The mixture will look almost like glue.) While still beating, add the egg and beat until incorporated. Then add the cheeses, a small handful at a time, beating, until incorporated. (The mixture will by sticky and slightly stiff.)
Use a small ice cream scoop or heaping tablespoons and scoop the dough out onto the prepared baking sheet, leaving at least 1inch between them. Moisten the palm of your hand with water and pat each scoop into a slightly rounded mound.
Bake until they become puffed up, golden on top, deeply golden on the bottom and feel relatively light when picked up and dropped on the baking sheet, rotating about halfway through baking, 20 to 24 minutes. Let cool for at least a few minutes then eat warm or at room temperature.
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