Boil potatoes in salted water until fork-tender, about 15 minutes. Drain well and mash until smooth.
Stir in both cheeses, garlic powder, cumin, paprika, chili powder, salt, and pepper. Mix until creamy.
Warm tortillas to make them flexible.
Place 2–3 tablespoons of potato mixture on each tortilla, then roll tightly into taquitos.
For baking: Place taquitos on a baking sheet, brush with oil, and bake at 425°F (220°C) for 15–20 minutes, until crisp.
For frying: Heat ½ inch of oil in a skillet. Fry taquitos seam-side down until golden brown, about 2 minutes per side. Drain on paper towels.
Serve hot with salsa, sour cream, or guacamole.
