Heat a large skillet over medium-high until it's ripping hot. Add the ground beef and leave it alone, no stirring yet. You want a hard, dark sear on one side before you break it up. Don't rush this part; it's doing more for the final flavor than you'd expect.
While the beef sears, set a large pot over medium heat.
Once the crust has formed, break the beef into small, pea-sized pieces and keep cooking until no pink remains.
Drain the fat.
Add the drained beef to the pot along with the onion, celery, green chilies, tomatoes, pinto beans, kidney beans, tomato sauce, water, broth, vinegar, salt, pepper, chili powder, and cumin. Stir to combine.
Bring to a boil, then drop the heat to a low simmer.
Simmer uncovered for about 2 hours, stirring every 15 to 20 minutes, until it's thick and the flavors have come together.