Place the diced pork belly in a large Dutch oven over low heat. Render slowly until golden and crisp and the fat has released. Remove the pork belly with a slotted spoon and set aside, leaving the fat in the pot.
Increase heat to medium and add the onion, carrot, and celery with a pinch of salt. Cook until very soft and lightly caramelized, about 10–12 minutes. Add garlic and cook briefly until fragrant.
Add the ground venison and ground pork. Brown deeply, allowing the meat to sit undisturbed at times to develop flavor. Return the pork belly to the pot.
Push the meat mixture to the sides of the pot and add the tomato paste to the center. Cook until dark, brick red, and caramelized.
Deglaze with red wine, scraping up any browned bits from the bottom of the pot. Simmer until reduced by about half.
Stir in the milk and allow it to gently simmer until mostly absorbed.
Add canned tomatoes, broth, bay leaf, thyme and rosemary (tied in a bundle), Parmesan rind, and a pinch of nutmeg. Bring to a gentle simmer.
Reduce heat to low, partially cover, and simmer for 3–4 hours, stirring occasionally. The sauce should become thick, rich, and deeply aromatic.
Remove bay leaf, rosemary sprig, and Parmesan rind. Crush the tomatoes. Stir in butter, grated Parmesan, and fresh basil. Taste and adjust salt and pepper.
Cook fresh pasta in well-salted water until just tender. Transfer pasta directly into the sauce with a splash of pasta water and toss gently until coated.