Cook the onion in a spoonful of the oil over medium heat until soft, about 4 minutes. Stir in the cumin, chili powder and salt, then the chicken, and cook 2 minutes more. Take it off the heat and mix in the cheese so it binds as it cools.
{'Warm the tortillas until fully pliable': 'either wrap 6 at a time in a damp towel and microwave 30 seconds, or pass each one through hot oil for 5 seconds. A cold tortilla will crack when rolled.'}
Working with two or three warm tortillas at a time, put about 2 tablespoons of filling in a line across the lower third of each.
Roll each one up tightly into a tube and set it seam side down on a tray. Keep the rest covered so they stay warm and flexible.
Heat the oil in a small skillet to 350F, deep enough to come about a third of the way up a taquito.
Fry in batches, seam side down first, 1.5 to 2 minutes, then turn and fry 1 to 1.5 minutes more, until deep golden and firm.
Lift onto a rack to drain rather than onto paper towel, so the underside stays crisp.
Serve hot, with shredded lettuce, crema and salsa, or with guacamole for dipping.