Place a large pot over medium-high heat. Combine 2 lb beef (or beef/pork mixture), onions and garlic. Cook until beef is brown and onions/garlic are cooked through.
While beef is cooking, place chopped carrots, celery, and 1/2 of the crushed tomato can in a blender or food processor. Blend/process until pureed.
Once beef is fully browned, add tomato paste and mix well to incorporate; saute for another 1-2 minutes.
Add carrot/celery/crushed tomato puree, white wine, diced tomatoes, the rest of the crushed tomatoes, salt, pepper, italian seasoning, parsley, and thyme. Mix well.
Cover with a slight crack for venting and simmer for 45 minutes to an hour.
Add grated parmesan and simmer for another 30 minutes.