Broil or grill chiles until blistered. Cover and steam for 10 minutes, then peel off the skins.
Cut a lengthwise slit in each chile and gently remove the seeds.
Fill peppers with shredded cheese, reserving some for topping.
Place stuffed chiles seam-side down in a baking dish.
Combine tomatoes, green chiles, broth, oregano, garlic, garlic powder, and onion in a saucepan. Simmer for 10 minutes.
Preheat oven to 375°F. Pour sauce over peppers, sprinkle with remaining cheese, and bake uncovered for 25 minutes until bubbly and golden.
Let rest for 5 minutes before serving warm.