Adjust oven racks to lowest and middle positions and heat oven to 450 degrees.

Heat a 5 to 6-quart heavy Dutch oven over low heat.

Meanwhile, place roast in a large bowl; coat with 1 tablespoon of oil and season with 1 tablespoon of the cumin and a generous sprinkling of salt and pepper. Mix chiles, chili powder, remaining 1 teaspoon of cumin, and oregano in a small bowl.

A few minutes before searing, increase heat to a strong medium-high until wisps of smoke start to rise from the pan. Add roast; sear, turning only once, until both sides form an impressive brown crust, about 8 minutes total. Transfer roast to a plate; set aside. Add garlic to the now empty pot; sauté until fragrant and golden, about 30 seconds. Add chili mixture; sauté to intensify flavor, another 30 seconds. Add chicken broth, bring to a simmer; return roast to the pot.

Using 2 potholders to protect hands, place a sheet of heavy-duty foil over the pot, pressing on the foil so that it touches the stew. Seal foil around the edges; repeat with a second sheet of foil to completely seal. Turn burner on medium-high until you hear juices bubble. Set pot on middle oven rack; cook for a total of 1 1/2 hours. Remove roast from oven, cool to room temperature, and shred into bite size pieces. About 30 minutes before roast is done, toss onions and peppers with remaining 2 tablespoon of oil and sprinkle generously with salt and pepper on a baking sheet large enough for vegetables to fit in a single layer. Place pan on bottom oven rack; cook until tender-crisp, about 30 minutes.

When ready to serve, gently warm meat and peppers and onions over low heat. Serve with warm tortillas*, bowls of sour cream, cilantro sprigs, and lime wedges.

*Of course you can always microwave tortillas, but I prefer to oven-steam them. For each 8 tortillas, lay a damp paper towel on a 24- by 18-inch piece of heavy-duty foil. Set 2 stacks of 4 flour tortillas each side by side on towel. Cover with another damp paper towel; seal foil completely. Warm in a 350-degree oven until steamy, about 5 minutes.