Preheat oven to 350 degrees. In a heavy pot with a tight-fitting lid, stir together chiles, ketchup, 1 cup water, garlic, oregano, 2 teaspoons salt, and 1/4 teaspoon pepper.

Cut beef into 4 equal pieces. Add to pot, and turn to coat. Cover, and bring to a boil; transfer pot to oven. Bake, covered, until beef is fork-tender, about 2 1/2 hours.

Transfer beef to a bowl. With a large spoon, skim off and discard fat from cooking liquid. Shred beef with two forks; moisten with cooking liquid as needed. Season with salt and pepper. Serve beef with tortillas and desired toppings.