Finely dice the onion and celery, grate the carrot, and mince the garlic. Measure out tomato paste, spices, wine, stock, milk and have the canned tomatoes ready.

Soften vegetables

Heat a large heavy-bottomed pot or Dutch oven over medium heat. Add the olive oil and when shimmering add the diced onion, grated carrot and diced celery. Cook, stirring occasionally, until the vegetables are softened and the onion is translucent, about 6–8 minutes. Add the minced garlic in the last 1 minute and stir until fragrant.

Brown the meat

Increase heat to medium-high. Add the ground beef and ground pork to the pot. Break the meat into pieces with a spoon and cook, stirring occasionally, until browned and no longer pink, about 6–8 minutes. Let excess fat render; if there is excessive fat (more than 3 tbs), spoon off and discard all but 2 tbs.

Develop flavor with tomato paste

Push the meat and vegetables to the side to create a clear patch in the bottom of the pot. Add the tomato paste to the hot area and cook, stirring constantly, for 1–2 minutes until it darkens slightly — this caramelizes the paste and deepens flavor. Then stir the paste into the meat and vegetables.

Deglaze

Pour in the red wine (if using) to deglaze the pan, scraping any browned bits from the bottom with a wooden spoon. Let the wine reduce by half, about 2–3 minutes. If not using wine, add 2–3 tbs of stock to deglaze similarly.

Add tomatoes and seasonings

Stir in the crushed tomatoes, beef or chicken stock, dried oregano, dried basil, dried thyme, bay leaf, sugar (if using), salt and pepper. Bring the sauce to a gentle simmer.

Long, gentle simmer

Reduce heat to low so the sauce barely bubbles. Partially cover the pot with a lid set slightly ajar. Simmer gently, stirring occasionally, for at least 45 minutes and up to 2 hours for deeper flavor. If the sauce becomes too thick, add a splash of stock or water. Taste and adjust salt and pepper as the sauce concentrates.

Finish with milk and herbs

About 5 minutes before serving, stir in the milk or cream and chopped fresh parsley. This softens the acidity and rounds the sauce. Remove and discard the bay leaf. Check final seasoning and add more salt or pepper if needed.

Serve

Serve the meat sauce hot over pasta, polenta, or use as a lasagna layer. Top with grated Parmesan and extra chopped parsley if desired. Leftover sauce cools, then refrigerate in an airtight container for up to 4 days or freeze for up to 3 months.