Break ground beef into small pieces in a large pot over medium heat; cook and stir until beginning to brown, 3 to 5 minutes.
Add onion, bell peppers, and carrot; cook and stir until the vegetables begin to soften, 5 to 7 minutes.
Add zucchini and squash; cook and stir until beef is completely browned, 3 to 5 more minutes.
Drain excess liquid from the pot.
Stir in crushed tomatoes, kidney beans, black beans, diced tomatoes, corn, and garlic; bring to a boil.
Stir in chili powder, brown sugar, paprika, oregano, cayenne pepper, cumin, salt, and black pepper.
Reduce the heat to low, cover, and simmer for 30 minutes.
