Season the beef with salt and pepper. In a large soup pot or a Dutch oven, heat the oil over medium-high heat. Add the beef in batches, and brown a few sides, about 8 minutes per batch (not every side has to be browned; better to caramelize a few sides well and let the rest just be). Transfer the meat with a slotted spoon to a plate as it finishes browning.
Drain off all but a couple of teaspoons of the fat from the pot, add the onions, and sauté over medium heat for 5 minutes, until the onions are tender. Add the garlic and sauté for one more minute, until you can smell the garlic. Add the chili powder, then stir in the tomato puree and the beef broth, return the browned beef cubes to the pot, and bring to a simmer over medium-high heat.
Reduce the heat and simmer, partially covered, for about 3 hours, until the beef is very tender. Add ½ to 1 cup of water towards the end if the sauce is too thick or the mixture looks too dry. When it is all tender, you can remove a cup of two of the beef cubes and shred them with two forks, and then stir that back into the pot to thicken up the sauce a bit, if desired.
Serve hot in bowls, with the accompaniments of your choice.
Notes
Not every side of the cubes of beef has to be browned. You can just caramelize a few sides well and let the rest just be.
Cook this chili low and slow so the meat can become very soft and the liquid thickens into a sauce and doesn’t just evaporate.
The sauce that binds together this chili is thick. If it gets too thick, stir in ½ to 1 cup water towards the end, especially if it starts to stick to the bottom of the pot.
Shredding some of the cubes of super tender beef at the end gives the sauce some more texture.
I serve my Texas Red Chili over rice with what I think of as traditional chili toppings — cheese, sour cream, avocado — which I also gather are somewhat debatable toppings in Texas.