Heat olive oil in a large sauté pan on medium high heat. Add the minced carrots and sauté for 5 minutes.
Add the chopped onion and celery. Cook, stirring occasionally until onions are translucent, about 5 more minutes.
Add the minced garlic and cook for 30 more seconds. Remove from heat. Remove vegetables from the pan, with a slotted spoon, and set aside in a bowl.
Using the same pan (to get all the flavor infused into the meat), add the ground beef. Cook over medium heat, breaking it up with a wooden spoon, until browned and cooked. Do not go overboard stirring the ground beef. Let it cook for a bit to get golden, crispy brown, before gently mixing. This will make the meat even more flavorful! Use a slotted spoon to remove the ground beef from the pan, and add it to the veggies. If you're pan wasn't big enough to cook all the meat at once, add the remaining meat to the pan and cook until brown.
Strain off the grease.
Return the cooked ground beef and vegetables to the pan. Use a wooden spoon to break up any chunks of ground beef into smaller bits.
Add the ketchup, tomato sauce, Worcestershire sauce, vinegar and brown sugar to the pan. Stir to mix well. Add ground cloves, thyme, and cayenne pepper.
Lower the heat to medium low and let simmer for 10 minutes. Adjust seasonings to taste.
Serve with toasted hamburger buns.