Heat oil in a large skillet over medium heat. Sauté onions until softened, about 4 minutes, then add garlic and cook another minute until fragrant. Stir in shredded chicken, cumin, chili powder, salt, and pepper.

In a medium bowl, whisk together sour cream, cream of chicken soup, diced green chiles, and chicken broth until smooth.

Warm tortillas in the microwave wrapped in damp paper towels for 30 seconds, or heat them one by one in a dry skillet.

Preheat oven to 350°F. Spread 1/2 cup of sauce in the bottom of a greased 9x13 baking dish. Place about 1/4 cup chicken filling down the center of each tortilla, sprinkle with cheese, then roll tightly and place seam-side down in the dish.

Pour remaining sauce over enchiladas, ensuring they're well covered. Sprinkle with remaining cheese. Bake for 20-25 minutes until bubbly and cheese is golden. Let rest 5 minutes before serving.