To fry the tortillas, heat a non-stick skillet over medium-high heat. Brush each side of the tortilla with a bit of oil. Fry them one by one, flipping occasionally until they are no longer white and just start to lightly brown. They can be a bit crispy, but not too much or they will crack as you roll them.
Assemble the tortillas as you fry them. Fill them with a good amount of chicken, making sure you can still tightly roll them up. Place into the baking dish, seam-side down. Continue to fry and roll the tortillas, adjusting them in the baking dish, if needed.
Next, pour the salsa verde over top. Spread the salsa to cover the enchiladas. You might not need to use all of the salsa, just make sure it comes at least half way up the enchiladas. As it cooks, the tortillas will absorb some of the salsa.
Sprinkle the cheese over top and bake for about 15 minutes.