Heat oil in a large Dutch oven or sauce pot over medium heat. Add grated carrots and onions and cook for a few minutes. Make a well in the center of the mixture, and then add in the ground beef. Cook for a few minutes until brown, gradually stirring it into the carrot mixture.
Add oregano, Italian seasoning, and basil. When the meat is browned and combined with other ingredients, make another well. Add tomato paste and let it heat. Add garlic and stir to combine.
Make a well in the center of the mixture and add red wine. Stir together. Add Worcestershire and stir, then add 2 cans tomato puree.
Finally, pour in milk, stir, and let simmer for one to 2 hours—or longer.