Heat olive oil in a large pot over medium. Add onion, carrot, and celery; cook 8–10 minutes until soft. Stir in garlic and cook 1–2 minutes more.
Add the ground beef, breaking it up with a spoon. Cook until it is browned all over, about 10 minutes. Season with salt and pepper.
Add the tomato paste to the browned beef and cook for 2–3 minutes, until it deepens in color and develops a rich aroma.
Pour in the red wine, scraping up any browned bits from the bottom of the pot. Simmer for about 5 minutes, until reduced by half.
Add the crushed tomatoes, oregano, and bay leaf. Reduce heat to low, cover partially, and simmer for at least 1 hour (up to 4), stirring occasionally. Keep the heat low so the sauce bubbles gently without burning on the bottom.
About 15 minutes before serving, bring a large pot of salted water to a boil. Cook the tagliatelle until al dente, following the package instructions.
Stir in the milk and ¼ cup Parmesan. Simmer for 5 minutes, then adjust seasoning with salt and pepper.
Drain the pasta, reserving ½ cup of water. Toss with the ragù, adding pasta water as needed to loosen. Top with fresh herbs and more Parmesan.