Preheat the oven to 400 degrees F. Heat a large, heavy-bottom, ovenproof skillet or sauté pan over medium-high heat. Meanwhile, pat the pork chops dry with paper towels and sprinkle them on both sides with salt and pepper to taste and the fresh herbs.
Add the oil to the hot skillet and as soon as the oil is hot enough to swirl around easily, add 1 tablespoon of the butter and the pork chops, spacing the chops about 1 inch apart. Cook the chops undisturbed until their undersides are golden brown, 2 to 3 minutes. Use tongs to turn them over and sear about 1 minute more.
Transfer the pan to the oven and roast until the chops are cooked through but still slightly pink at the center, about 12 to 15 minutes.
Remove the pan from the oven, transfer the chops to a platter, and cover them with aluminum foil to keep them warm while you make the sauce.
Pour off all of the fat from the skillet. Return the skillet to the stovetop over medium-high heat and pour in the port. With a wooden spoon, stir and scrape to deglaze the pan deposits. Add the dried cranberries and continue simmering the Port briskly until it reduces to about half its original volume, about 5 minutes.
Stir in 1 tablespoon of the hoisin sauce or barbecue sauce and continue simmering, stirring frequently, until the mixture is thick enough to coat the back of a spoon; taste the sauce and, if you like, stir in a little more hoisin or barbecue sauce. Then whisk in the remaining butter, a piece or two at a time, until the sauce looks creamy and glossy. Taste the sauce and, if necessary, add a little more salt and pepper to taste.
Return the pork chops to the skillet, turn them in the sauce to coat them well, and continue simmering until the chops are heated through, 1 to 2 minutes more.