In a Dutch oven, combine bite-sized round steak pieces, water, salt, pepper, and bay leaf.

Bring to a boil, then reduce heat to a simmer.

Cover and simmer until the beef is tender, approximately 1-2 hours, adding water if necessary to prevent burning.

Remove the beef from the pot and let it cool slightly.

Pour the broth into a separate container and reserve.

In the same Dutch oven, cook sliced onions and chopped garlic in olive oil over medium heat until the onions are tender.

Shred the cooled beef into strands.

Return the shredded beef to the Dutch oven.

Add chopped green chilies, chopped tomatoes, green pepper squares, and the reserved broth.

Bring the mixture to a boil, then reduce the heat and simmer uncovered for 30 minutes, allowing the flavors to meld.

Serve the Ropa Vieja hot over white rice.