Place the ribs on a baking sheet and season all sides generously with salt and pepper.
Lightly coat the bottom of an oven-safe pot (approximately 10 to 12-inch diameter), with olive oil. (A Dutch Oven is perfect.) Place the pot over high heat. Add the ribs to the pot once it's very hot, about 4 at a time -- you should hear a sizzling sound, and if you don't, it's not hot enough. Wait until it's very hot and listen for the sizzle! Searing the meat this way seals in the juices, caramelizes the surface, and reduces the overall cooking time. Brown the ribs very well, about three minutes per side. Remove the ribs from pot, place them on a plate, and set aside. Repeat this until all of the ribs are browned.
Add the onions to the pot and cook over medium-high heat, stirring every couple of minutes, until they are golden and are soft, about 10 minutes. Add the garlic and cook for another 5 minutes. Add the fresh thyme and cinnamon and cook for another minute or so, until it's very aromatic. Now add the pumpkin and cook until it begins to brown, about 5 minutes. The bottom of your pot will become brown, too, and this is okay. In fact, it's great! It is flavor!
Pour in the stock and wine and use a deglazing spatula (a wooden one with a flat edge is best), to scrape the bottom of the pan, working all the wonderful flavor back into the sauce. Bring to a boil, then lower to a simmer and do not cover.Preheat the oven to 325°F.Let the mixture simmer until it has reduced by about ⅓, about 20 minutes.
Return the ribs to the pot and gently stir them into the sauce. Cover the pot and place in the preheated 325°F oven. Braise until the meat is very tender and easily comes off the bone, about 2 hours. Turn the ribs over halfway through the cooking time.
If the braising liquid is as think as you'd like it to be, then it's ready. Otherwise, to thicken the liquid further, remove the lid, place the pot over low heat on the stove, and let it simmer until it's as thick as you'd like.
Season with salt and freshly ground black pepper to taste. (Here's How to Season to Taste.)Serve with the braising liquid.