Begin by heating olive oil or butter in a heavy-bottomed pot over medium heat. Once melted and hot, add the finely chopped onion, celery, and carrot. This is your soffritto, and it forms the aromatic base of the sauce. Sauté gently for 10 to 15 minutes until the vegetables are soft and translucent. Stir often and don’t rush—this step is crucial to releasing natural sweetness and depth.

Next, increase the heat slightly and add the ground beef and veal or chicken. Break it up with a wooden spoon and cook slowly, allowing it to brown deeply and evenly. This may take 10 to 15 minutes. As the meat cooks, season lightly with salt and pepper, and continue stirring to prevent burning or clumping.

Once the meat is browned and most moisture has evaporated, stir in the tomato paste and cook for 3 to 5 minutes to develop its flavor. You’ll notice the paste deepen in color as it caramelizes. Then, slowly pour in the milk and stir gently. Let the mixture simmer until the milk is mostly absorbed—this neutralizes the acidity of the tomato and tenderizes the meat.

After the milk is reduced, begin adding the warm broth a ladle at a time. Stir, reduce the heat to low, and let the sauce simmer uncovered for 2 to 3 hours. Stir occasionally and add more broth if the sauce becomes too thick. The goal is a rich, silky texture—not watery and not dry.

Taste and adjust the seasoning as needed. When finished, your ragù should be thick, creamy, and a beautiful deep rust color, with no visible liquid separating from the meat.