Heat 2 tablespoons of the oil in an ovenproof, heavy, large covered pot over high heat.(If you don't have a large pot that goes from stovetop to oven, simply prepare on stovetop, and then transfer to a covered casserole before baking).
Add half of the pork cubes; sprinkle with half of the salt and half of the black pepper. Cook pork until starting to brown, stirring often. Remove pork.
Repeat with remaining pork cubes, salt and black pepper, adding more oil if necessary.
Drain drippings from pot.
Heat remaining 1 tablespoon oil in the same pot over medium heat. Cook onion in hot oil until tender.
Stir in undrained chiles and garlic; cook for 2 minutes.
Return pork to pot. Add chicken broth.
Cover and put in oven to bake for 1 hour.
Serve pork in tortillas topped with Cheddar cheese, tomato and sour cream if desired.