In a bowl, combine the potatoes, onion, flour, parmesan, egg yolk, salt and garlic powder.
In a deep skillet, heat 1 inch oil over medium-high heat until it registers 350 degrees on a deep-fry thermometer. Form rounded tablespoons of the potato mixture into balls, squeezing out the excess moisture. Working in batches, drop the mixture into the oil and fry until golden, about 5 minutes. Drain on paper towels.
Place the asiago and rosemary in a large bowl. Working in batches, toss the tater tots in the cheese mixture.