Warm the olive oil in a large Dutch oven over medium heat.
Add the onion, carrots, and celery, and cook for 8 to 10 minutes until soft and lightly golden.
Stir in the garlic and cook for 1 minute more, until fragrant.
Add the ground beef, breaking it into small crumbles as it cooks, until browned and no longer pink.
Drain excess grease if needed.
Stir in the tomato paste and cook for 2 to 3 minutes until it darkens slightly, developing a deeper, richer flavor.
Pour in the red wine, scraping up any browned bits from the bottom of the pot.
Simmer until almost all of the liquid has reduced.
Add the crushed tomatoes, beef broth, milk, Italian seasoning, thyme, salt, pepper, red pepper flakes, and Parmesan rind.
Bring everything to a gentle simmer.
Reduce the heat to low and cook partially uncovered for 45 to 60 minutes, stirring occasionally, until thick and rich.
Remove the Parmesan rind, stir in the grated Parmesan cheese, and adjust the seasoning to taste.
Serve over freshly cooked pasta and garnish with more Parmesan and chopped herbs.