Place chopped plum tomatoes in a food processor; pulse until pureed. Transfer to a Dutch oven over medium heat. Add vegetable stock, green bell peppers, tomato paste, mushrooms, vinegar, and oil. Bring to a boil; reduce heat and simmer until saucy, 1 1/2 to 2 hours.
Heat a large skillet over medium-high heat. Cook and stir ground beef in the hot skillet until browned and crumbly, 5 to 7 minutes. Drain and discard grease. Transfer cooked beef to the Dutch oven.
Place onion, parsley, shallot, garlic, habanero peppers, Italian seasoning, fennel seeds, sugar, and basil into the Dutch oven. Cover and continue to simmer until vegetables are tender, 12 to 15 minutes more.