Season both cuts of beef with 1 1/2 teaspoons salt and heat the oil in a Dutch oven over medium-high heat.
Brown the chuck for 6 minutes, transfer it to a plate, then cook the ground beef for 6 to 8 minutes until it reaches 160°F.
Return the chuck and stir in half the ancho powder, half the New Mexico powder, 1 teaspoon cumin and the garlic powder for 30 seconds.
Add the tomato sauce and broth and simmer partly covered for 75 minutes, then add the remaining chile powders, cumin and salt and cook for 25 minutes until the chuck reaches at least 145°F and is tender.
Whisk the masa harina with the warm water, stir it in, and simmer uncovered for 10 minutes until the gravy is smooth and cohesive.