Season chops with salt and pepper. Heat oil in a large, heavy frying pan over medium-high heat. Lay chops in pan and cook until browned, turning once, 2 to 4 minutes per side. Transfer to a plate and cover loosely with foil.
Add sage leaves and fry until crisp, about 30 seconds. Drain on paper towels.
Reduce heat to medium-low and add butter, chopped sage, shallots, and 4 thyme sprigs to the pan. Cook, stirring occasionally, until shallots are soft and lightly browned, 6 to 10 minutes.
Increase heat to medium-high and add cider. Cook, stirring and scraping to release browned bits, until cider is reduced by two-thirds, 3 to 4 minutes. Reduce heat to medium-low, stir in cream, and boil 2 minutes to thicken sauce.
Return pork chops and juices to pan in a single layer, spooning some shallots and liquid over chops. Cover and cook until chops are only barely pink in center (cut to test), 4 to 5 minutes more (they will continue to cook off the heat). Remove bare thyme sprigs (most of the leaves will have fallen into the sauce).
Season with salt and pepper to taste and top with fried sage and remaining thyme sprigs.