Brown the ground chuck in a large pot over medium-high heat for 8–10 minutes. Drain and set aside.
Brown the hot breakfast sausage in the same pot. Leave the rendered sausage fat in the pot.
Add onion, jalapeños, and garlic. Cook for about 5 minutes until softened and fragrant.
Add diced tomatoes, tomato sauce, Hatch green chiles, tomato paste, and Williams chili mix. Stir well.
Return the ground chuck to the pot. Cover and simmer gently for 1 hour, stirring every 15 minutes.
Stir in the three cans of chili beans.
Simmer uncovered for another 30 minutes, stirring occasionally.
Taste, adjust seasoning if needed, and rest for 10 minutes before serving.