Preheat the oven to 400°F (204°C) if baking, or preheat the air fryer to 400°F (204°C) if using an air fryer.
In a large mixing bowl, combine the shredded chicken, cream cheese, shredded Monterey Jack (or chosen cheese), salsa, chili powder, garlic powder, cumin, and salt and pepper to taste; mix until evenly combined.
Lay the tortillas flat and evenly divide the chicken mixture among the 12 tortillas, placing filling in a line near one edge, then roll each tortilla tightly to enclose the filling.
Place rolled taquitos seam-side down on a sheet pan (for oven) or prepare them for the air fryer basket in a single layer without overcrowding.
Lightly brush each taquito with oil or spray all sides with cooking spray to promote browning and crisping.
To bake: arrange taquitos in a single layer on the sheet pan and bake at 400°F for 15–20 minutes, or until the outsides are golden and very crispy.
To air-fry: place taquitos in a single layer in the air fryer and air-fry at 400°F for 12–15 minutes, checking at 12 minutes to avoid burning, until crispy.
Remove taquitos when crispy, let cool slightly, and serve with optional toppings such as sour cream, guacamole or avocado, tomato, cilantro, and lime.