Preheat Oven to 325 degrees. Put 3 Tbsp Olive Oil in a Dutch Oven or other large oven proof pot on medium-high heat. Brown Pork Shoulder pieces in the pot for 3-4 minutes on each side. Remove Pork Shoulder and set aside on a plate. Add Carrots, Celery, Onion, Mushrooms, and dried Herbs to the pot, sauté until onions are translucent. Add Garlic and cook for 2-3 minutes to soften. Add Red Wine to deglaze the pan while scraping the bits off the bottom and cook for 2 minutes. Add Crushed Tomatoes, Tomato Paste, Sugar, Salt, and Pepper. Stir to combine all ingredients and bring to a boil.
Place Pot into the Oven and let it cook for 3-4 hours. Give it a stir and check for moisture once in a while. You might need to add a little bit of water to keep it from getting too dry. Your house will smell amazing by this point!
Remove from Oven and place on stovetop. Break up meat using an immersion blender or by placing in a food processor and giving it several pulses to incorporate all ingredients. Place back into the pot and set aside to let the flavors meld.
Bring a large pot of heavily salted water (should taste like the Ocean) to a boil. Add Pasta and cook per directions on the package. Once cooked to your liking, drain the pasta. Add Pasta to the Sauce and heat prior to serving.
Dish up into a large serving dish or individual servings and garnish with Parmesan Cheese and Parsley. Mangia!
Don't turn on your oven. Follow all instructions above and brown meat and veggies on Sauté mode before adding Tomatoes. Once everything is combined, place on the lid and cook for 45 minutes. Let the pressure release naturally for 15 minutes, then manually release the pressure. Follow remaining instructions above after the step "Remove from Oven and place on stovetop".