Preheat oven to 350 degrees F. Chop chicken; set aside. In a blender or food processor combine tomato, onion, chile peppers, and garlic; cover and pulse with several on/off turns until finely chopped. In an extra-large skillet heat the 2 tablespoons oil over medium-high heat. Add chicken; cook and stir for 2 minutes. Add tomato mixture and salt. Bring to boiling; reduce heat. Simmer, uncovered, for 5 to 7 minutes more or until liquid is nearly evaporated and chicken is cooked, stirring occasionally. Remove from heat; cool slightly. Meanwhile, clean blender or food processor. Transfer chicken mixture to the clean blender or food processor. Cover and pulse with several on/off turns until chicken is finely chopped; set aside.
In a large skillet heat 1/2 inch of vegetable oil over medium heat to 365 degrees F.
Meanwhile, lightly coat both sides of each tortilla with cooking spray. Stack tortillas; wrap in foil. Bake for 15 minutes. Decrease oven temperature to 200 degrees F.
For each taquito, spoon about 3 tablespoons of the chicken mixture across the lower third of each warm tortilla; add 2 tablespoons of the cheese. Roll up tortillas as tightly as possible; secure with wooden toothpicks.
Fry taquitos in hot oil, four at a time, for 2 to 3 minutes or until crisp and golden brown, turning occasionally to brown evenly. Drain on paper towels. Transfer fried taquitos to a baking sheet and keep warm in a 200 degrees F oven while frying remaining taquitos.
If desired, serve taquitos with salsa, sour cream, and/or guacamole.