Warm the oil in a large skillet over medium heat. Sauté the onion for 2-3 minutes until it turns translucent, then add the garlic, oregano, and cumin, cooking just until aromatic, roughly a minute. Take the skillet off the heat and mix in the green chiles.

Transfer the chile mixture to a large bowl along with the chicken, ⅓ cup of the salsa verde, and the cilantro. Fold in about half the cheese and season with salt and pepper.

Spoon a generous portion of the filling down the center of each tortilla, roll tightly, and arrange seam-side down in the prepared dish. Once all the tortillas are filled and rolled, pour the remaining salsa verde over the top and scatter the rest of the cheese evenly across.

Bake for 35-40 minutes, until the cheese is melted and bubbling.

Let the enchiladas rest a few minutes, then serve warm with a dollop of sour cream on top.