Heat 2 Tbs. of the oil in a heavy-duty 6-quart pot over medium-high heat until shimmering hot. Season the beef with 1-1/2 tsp. salt and 3/4 tsp. pepper. Cook half of the beef, undisturbed, until browned, 2 to 3 minutes. Break up the meat and cook, stirring or turning occasionally, until well browned, 2 to 3 minutes. Transfer to a large plate. Add another 1 Tbs. oil to the pot, and brown the remaining beef; transfer to the plate along with any liquid from the pot.
Add the remaining 1-1/2 Tbs. of oil, the onion, and garlic to the pot. Sprinkle with 1/2 tsp. salt and cook over medium heat, stirring occasionally, until softened and lightly browned, about 5 minutes. Stir in the bell pepper, jalapeño, chili powder, cumin, tomato paste, and New Mexico chile powder and cook, stirring, until fragrant, 1 to 2 minutes.
Pour in the beer, turn the heat up to high, and cook, scraping the bottom of the pot to loosen any browned bits, until most of the liquid is evaporated, about 2 minutes.
Add the canned tomatoes and beef broth and bring to a simmer.
Turn the heat down to medium low. Purée 1-1/2 cups of the beans in a blender or food processor, adding a little stewing liquid as needed, and then stir the puréed beans into the stewing liquid in the pot. Add the remaining whole beans. Cover and simmer, stirring occasionally, for 30 minutes. Add the ground beef back to the pot, and cook for 30 minutes more. If the chili gets too thick, thin it with a little water.
Add the corn and zucchini to the chili and cook until tender, about 10 minutes.
Stir in the lime juice, and season with salt and pepper to taste.
Serve with the garnishes.