Heat olive oil in a large, heavy-bottomed pan over medium-high heat. Add the diced onion, carrots, and celery, cooking for 5-6 minutes until the vegetables soften and the onion becomes translucent. Stir in the minced garlic and cook for another minute until fragrant.

Push the vegetables to one side of the pan and add the ground beef. Break it up with a wooden spoon, allowing it to brown without stirring for 2-3 minutes initially. Continue cooking, breaking up larger pieces, until the meat loses its pink color and develops a rich brown exterior.

Stir in the tomato paste and cook for 1 minute until it darkens slightly and becomes fragrant. Pour in the wine, scraping up any browned bits from the bottom of the pan. Let the wine simmer for 2-3 minutes to cook off the alcohol, then add the crushed tomatoes, bay leaves, oregano, and thyme.

Reduce heat to medium-low and let the sauce simmer for 10-12 minutes, stirring occasionally. Slowly pour in the milk, which adds creaminess and balances the acidity of the tomatoes. Season generously with salt and pepper, tasting as you go. The sauce is ready when it coats the back of a spoon and has reduced to a rich, clingy consistency.