Preheat oven to 450°F. Whisk eggs.
Cook tater tots in oil until golden, about 7 minutes. Drain.
Brown sausage, 4 to 6 minutes. Add eggs and cook until just set, 2 minutes.
Brush tortillas with oil. Sprinkle with cheese. Divide tots and egg mixture. Fold tortillas.
Bake until browned, 5 to 7 minutes. Cool 5 minutes. Slice and serve.