Pulse cheese in food processor until it is finely chopped and resembles coarse meal. Transfer to a large, wide bowl and whisk in the cornstarch, yucca flour, sugar and baking powder.
Add eggs and milk and stir until moistened. Using hands, gently knead the dough in the bowl until evenly combined. The dough should be smooth and firm but not dry. Form the dough into 24-1 1/2 inch balls and transfer to a waxed paper-lined baking sheet.
Fill a large Dutch oven with 2-inches of vegetable oil and heat the oil to 325F. Fry the buñuelos in two or three batches over medium heat, turning occasionally, until golden all over and cooked through, about 8 minutes.
Drain on paper-towel lined baking sheet and let cool for 15 minutes. Dust with confectioner's sugar, if desired, and serve warm.