In a large skillet, heat the olive oil over medium heat until shimmering. Add the butter and stir with a wooden spoon until melted. Add the onion, celery, and carrot and saute until tender, about 4 to 5 minutes.
Add the sausage and stir to break into smaller clumps. Sprinkle with the nutmeg and season with ½ tsp salt and ½ tsp pepper. Reduce heat to medium-low and cook until the sausage is almost fully cooked, about 8 minutes.
Add ½ cup of the half-and-half, stir well, and cook for 8 minutes, using a wooden spoon to incorporate the half-and-half into the sausage mixture.
Stir in the tomato paste. Use your hand to squeeze tomatoes into the sauce, mixing well. Add another ½ tsp salt and ¼ tsp pepper to the sauce.
Reduce the heat to low and cook for 45 minutes. Stir occasionally, adding the beef stock in increments to keep the sauce from not drying out. After simmering for 45 minutes, and after you've added all of the beef broth, stir in the remaining ½ cup of half-and-half.
Meanwhile, bring a pot of salted water to a boil. Add the pasta and cook until al dente, according to package instructions. If using fresh pasta, it will only need to cook for about 2 minutes. Be sure to save a least a cup of pasta water.
Add the pasta to the sauce in the skillet and toss until the strands are well coated with the sauce. Add reserved pasta water to help loosen the pasta and mix with the sauce. Serve at once with grated cheese passed at the table.