Season the beef with 1 teaspoon salt and pat it dry.
Heat the oil in a Dutch oven over medium-high heat and brown the beef in 2 batches for 5 minutes per batch.
Cook the onion for 5 minutes, then stir in the garlic and cumin for 30 seconds.
Return the beef, add the green chiles, broth and remaining salt, and simmer partly covered for 85 minutes until the beef reaches at least 145°F and is tender.
Whisk the masa harina with the warm water, stir it into the pot, and simmer uncovered for 10 minutes until lightly thickened.