Sear the MeatIn a large pot or Dutch oven, heat a drizzle of oil over medium-high heat. Sear the beef chuck roast and beef shank on all sides until browned. This step builds deep flavor into the broth.
Build the BrothAdd 7 cups of water, onion, garlic, bay leaves, 1 Roma tomato and salt. Bring to a boil. Skim off any foam that forms on the surface. Reduce heat to medium, cover, and simmer for 1 hour until the beef begins to turn tender.
Add Corn and Seasonings Stir in the corn pieces, beef bouillon, tomato bouillon, oregano and season with salt and black pepper. Cover and cook for 30 minutes.
Add Hearty VegetablesAdd the carrots and potatoes. Cover and cook for another 10–15 minutes until they begin to soften.
Add Tender VegetablesStir in the calabacitas, green beans, cabbage, and cilantro. Cover and simmer over medium heat for about 10–12 minutes, or until all vegetables are fork-tender and flavors are well blended.
ServeRemove bay leaves and garlic head if desired. Serve hot with warm corn tortillas, lime wedges, and sliced jalapeños on the side.