Bring 3 cups water to a boil in a medium saucepan. Whisk in the grits, 1/2 teaspoon salt and a few grinds of pepper. Reduce to a gentle simmer and cook, whisking, until thickened, 5 to 7 minutes. Stir in the cheese and pumpkin until smooth; season with salt and pepper. Remove from the heat and cover to keep warm.
Meanwhile, heat a large skillet over medium-high heat; add the vegetable oil. Season the pork chops with salt and pepper, add to the skillet and cook until browned on the bottom, about 3 minutes. Flip the pork and cook until almost cooked through, 2 to 3 more minutes. Add the butter and sage and cook until the butter is melted. Tip the skillet slightly and spoon the butter over the pork; cook, basting with the butter, until the pork is cooked through and the butter is golden brown, 1 to 2 more minutes. Remove the pork to a plate, leaving the butter in the skillet. Place the sage leaves on the pork chops; tent with foil to keep warm.
Return the skillet to high heat and add the shallot and chard stems. Cook, stirring, until tender, about 3 minutes. Stir in the chard leaves and cook until just wilted, 1 to 2 minutes. Add the vinegar and cook until dry, about 1 minute; season with salt and pepper. Divide the grits and chard among plates. Top with the pork chops.