Make the sauce base: In a bowl, whisk together chicken broth, heavy cream, Dijon mustard, Italian seasoning, onion powder, paprika, salt, and pepper. Stir in the minced garlic and Parmesan. Set aside.
Layer the pork: Place the pork pieces in your slow cooker or a large baking dish.
Scatter the butter in small pieces over the top.
Dump and go: Pour the sauce mixture over the pork. No need to stir.
Slow cooker method: Cook on Low for 6–7 hours or on High for 3–4 hours, until the pork is fork-tender.
Oven method: Cover the baking dish tightly with foil. Bake at 325°F (163°C) for 2–2.5 hours, until tender and bubbling.
Instant Pot method: Add everything to the pot.
Seal and cook on High Pressure for 25 minutes (pork loin) or 35 minutes (pork shoulder), then natural release for 10 minutes before venting.
Thicken the sauce (optional): If you want a thicker sauce, whisk cornstarch and cold water to make a slurry. Stir it into the hot sauce and cook for 5 minutes on High (slow cooker), 3–5 minutes simmering on the stovetop after baking, or sauté in the Instant Pot for 3 minutes.
Taste and finish: Adjust salt and pepper. Garnish with chopped parsley.
Serve: Spoon the pork and sauce over pasta, mashed potatoes, or rice.
Top with a little extra Parmesan if you like.