Start by sautéing diced onions and garlic in a skillet until fragrant. Stir in the softened cream cheese, diced green chiles, salsa verde, and sour cream. Once smooth, reserve half for topping later.
In a mixing bowl, combine shredded chicken with the remaining cream cheese sauce. Mix until the chicken is evenly coated for a rich and flavorful filling.
Spread a bit of sauce at the bottom of your baking dish to prevent sticking. Fill each tortilla with the chicken mixture and a sprinkle of shredded cheese, roll up, and place seam-side down in the dish.
Pour the remaining sauce over the top and sprinkle with more cheese. Cover with foil and bake at 350℉ for 25 minutes, removing the foil halfway through for a golden, bubbly finish.