Add the steak chunks to a large Dutch oven or heavy soup pot. Fill with water, leaving about 2 inches of space from the top.

Stir in salt, chopped garlic, and carrots. Bring to a boil over high heat.

Reduce heat to a gentle simmer and cook uncovered for 3–4 hours. Add water as needed to keep the meat submerged.

Once the meat is fork-tender, remove it and shred or chop it into bite-sized pieces, discarding excess fat.

Return the shredded beef to the pot. Add the green chile and red chile powder to infuse the broth with festive flavor.

Stir well and allow the chile to blend into the broth over medium heat for 5–10 minutes.

Drain and rinse canned hominy (or prepare fresh if using). Add to the pot with the beef and chile broth.

Simmer for an additional 30–40 minutes until the flavors have melded and the hominy is tender and chewy.

Taste and adjust seasoning with more salt if needed.