Place beef, carrot, cabbage, mint, parsley stems, garlic, peppercorns, and 1 teapsoon of salt in a large pot with water to cover (about 6 cups.) Add one of the bay leaves. Bring to a boil, reduce the heat to simmer. Cover and cook until the beef is tender, about 1 1/2 hours.
Remove from the heat and remove the beef from the broth. Reserve 1 cup of the broth for the vegetables. Strain and keep the remaining for another use. Discard the solids. When cool, remove the beef and shred by hand. Set side.
To prepare the onions and pepper, heat the oil in a large skillet over medium heat. Add the onion and bell peppers; cook until the onion is soft, 5 to 7 minutes. Add the garlic, ground cloves, ground allspice, and remaining bay leaf. Stir to combine. Add the tomato puree, reserved broth. Bring to a boil over high heat.
Add the shredded beef and stir to combine. Reduce the heat to simmer, and cook, stirring occasionally until the flavors are married, about for 15 minutes. Taste and adjust for seasoning with salt and pepper. Serve with rice or potatoes.