Allow pork to reach room temperature before seasoning. Rub with salt, pepper, flour, and cornmeal. Heat oil in skillet over medium-high and sear all sides until golden (~3–5 minutes each). Transfer meat to a roasting pan.

In roasting pan, melt butter. Stir in flour and cornmeal to form a roux; cook until just golden. Add onion, cumin, and oregano; sauté until fragrant and softened. Stir in tomatoes and chiles, then whisk in broth gradually.

Nestle pork into sauce, cover tightly, and roast at 250°F (120°C) for about 6 hours, until easily shredded.

Let the meat rest briefly before shredding. Stir pork back into chile sauce to absorb flavors.

Warm tortillas until flexible. Layer beans, shredded cheese, diced onion, and pork with sauce on each tortilla. Roll tightly with seam down. Option to smother extra sauce and cheese and broil briefly until bubbly.

Present smothered burritos hot. Add sour cream, cilantro, avocado, or lime for brightness.