Heat olive oil in a large Dutch oven over medium heat. Add pancetta and cook, stirring, until golden and fat is rendered, about 5 minutes. Add onion, carrot, and celery; season with 1/2 teaspoon salt and pepper. Sauté until vegetables are softened, about 8 minutes.

Increase heat to medium-high. Add ground beef, breaking it up with a wooden spoon. Cook, stirring occasionally, until meat is deeply browned, any liquid has evaporated, and the internal temperature reaches 160°F (71°C), about 10 minutes. Use a food thermometer to check.

Pour in white wine, scraping up any browned bits from the bottom. Let it bubble until nearly evaporated, about 2 minutes. Stir in milk and let it almost fully absorb, about 5 minutes. Then add crushed tomatoes, tomato paste, and nutmeg. Bring to a gentle simmer, then reduce heat to low. Cook, partially covered, for at least 1.5 hours, stirring occasionally. If sauce looks dry, add a splash of water or broth.

When the sauce is nearly done, bring a large pot of salted water to a boil. Cook tagliatelle until al dente according to package instructions. Reserve 1 cup pasta water, then drain pasta.

Add a few ladles of sauce to the drained pasta and toss vigorously, adding splashes of reserved pasta water as needed to loosen. Fold in 1/2 cup Parmigiano-Reggiano. Divide among bowls, top with remaining sauce, extra cheese, and a basil leaf.