Season pork generously with salt all over. Let sit at room temperature at least 1 hour before cooking.
Preheat oven to 325°. Heat oil in a large Dutch oven over medium-high. Add pork to pot and cook, undisturbed, until golden brown, 3–5 minutes. Turn and cook, reducing heat to medium if needed so it doesn't burn, until golden brown on all sides, about another 5 minutes. Remove pork from the pot and set aside.
Reduce heat to medium (if you haven’t already) and add onions, garlic, and red pepper flakes to the pot. Cook, stirring frequently, until the onions have softened, but not browned, about 5 minutes.
Add the tomato paste and pumpkin puree and cook for another 5 minutes, stirring frequently.
Add the white wine, using it to scrape up any of the browned bits that have accumulated at the bottom of the pan. Increase heat to medium high, still stirring frequently until the cooking liquid starts to boil. Cook for another 5 minutes to reduce a bit of the wine.
Turn off the heat, then add the milk and Parmesan cheese and stir to combine. Return the pork to the pot and add the sage and parsley. Transfer pot to oven and bake, uncovered, turning pork every 45 minutes, until meat is very tender, about 3 hours. (If using bone-in pork shoulder, you may have to increase your cooking time by another 30 minutes or so). Transfer pork to a cutting board and let rest for 15 minutes.
Using a spoon, skim off most of the fat from the braising liquid; discard sage and parsley. If desired, transfer the rest of the contents of the pot to a blender and puree to achieve a smoother sauce. Taste the sauce and adjust seasoning with salt and pepper, if needed.
Slice pork and transfer to a platter. Spoon sauce over and serve
Recipe by Allons-Eat! at https://www.allonseat.com/milk-braised-pork-with-pumpkin-and-parmesan/