Heat a little oil in a large skillet over medium heat. Add diced onion and cook for about three minutes until it softens and becomes slightly sweet. Then add garlic, cumin, and chili powder. Cook for another thirty seconds until the spices smell warm.
Next, add shredded chicken, sour cream, and ½ cup of salsa verde to the pan. Stir everything well and season with salt and pepper to taste. Remove the pan from heat and let the filling cool for a few minutes before rolling, as hot filling can tear soft tortillas.
Warm the tortillas. You can do this in a dry skillet for about 15 seconds per side, or wrap them in a damp towel and microwave for 30 seconds. Warm tortillas bend easily around the filling without cracking.
Preheat the oven to 375°F. Spread a thin layer of salsa verde on the bottom of a 9x13 baking dish. Lay a tortilla flat on a clean surface, spoon about a third cup of chicken filling down the center, and roll it up tightly. Place it seam-side down in the baking dish. Repeat this with the remaining tortillas, lining them up snugly next to each other.
Pour the remaining salsa verde over the rolled tortillas, making sure each one gets some sauce. Sprinkle shredded cheese generously over the whole dish.
Cover the baking dish with foil and bake for eighteen minutes. Then remove the foil and bake for another seven minutes until the cheese is bubbly and golden brown in spots. Let the dish rest for about five minutes before serving. Top with fresh cilantro and a squeeze of lime.