Heat oil in a skillet and add pork, and season with salt and pepper. Brown pork with a slotted spoon, transfer to a bowl and set aside. Add ground turkey to the skillet and brown. Transfer browned turkey to the bowl with pork and set aside.

In the same skillet, add onion, carrot, celery, and thyme; season with salt and pepper. Cook vegetables, over medium heat, until softened but not brown. Add garlic and continue cooking until fragrant, about 1 minute more.

Add tomato paste to skillet and cook, stirring constantly, until deep red and caramelized; about 3 minutes. Add pork and turkey to the skillet and stir. Then add wine and simmer until reduced by half. Stir in the undrained tomatoes and bring to a simmer. Continue cooking until sauce is thickened, about 7 minutes. Stir in broth and bring to a boil.

Reduce heat to low, place the lid askew, and simmer, stirring occasionally, until meat is tender and sauce is reduced; about 2 to 2 1/2 hours. Stir in a couple of tablespoons of milk from time to time. At the end of cooking, all of the milk should be absorbed to create a thick soup type of texture. If needed, remove the lid during the last 1/2 hour for the juices to reduce. Season to taste with salt and pepper.

Serve over pasta and garnish with freshly grated Parmesan cheese.