Cut the chuck roast into 3–4 large pieces. Generously season with salt and pepper. Let rest at room temperature ~20 minutes.

Preheat broiler to high. Remove stems/seeds from Anaheim and jalapeños (unless you want more heat). Place on a wire‑rack baking sheet, broil ~12–15 minutes turning once until blistered and charred. Transfer hot chiles to a covered bowl or sealed plastic bag to steam (~10‑15 minutes) to loosen skins. Peel and slice.

Heat oil in a heavy‑bottomed skillet or Dutch oven over medium‑high heat. Add beef pieces and sear on all sides (~4–5 minutes per side) until golden browned. Remove beef to a plate. In the same pot, add the reserved onion half and 4–5 garlic cloves; sauté briefly until aromatic.

Return beef to pot, pour in 6 cups water or beef broth. Bring to a simmer, reduce heat to low, cover and cook for ~1½‑2 hours (or ~35 minutes in a pressure cooker) until beef is fork‑tender.

While beef is cooking and chiles are steaming, dice potatoes and pat dry. In a separate skillet, heat 3‑4 Tbsp oil over medium heat; add potatoes, lightly season, and cook ~15 minutes stirring, until golden and tender. Add the minced garlic and diced onion and cook ~5 more minutes.

Shred the cooked beef. To a blender add the cooked onion & garlic from the beef pot, tomatoes, reserved jalapeños, oregano, cumin, salt and pepper. Blend until smooth. Pour the sauce into the beef/ potato skillet with the sliced green chiles and shredded beef. Add ~1½ cups of the cooking liquid from the beef pot. Stir to combine, then simmer ~20–25 minutes until sauce thickens and everything is coated.

Spoon beef‑chile‑potato mixture into bowls or onto tortillas. Garnish with fresh cilantro and serve with lime wedges and warm tortillas.