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Combine pepper and 1/4 teaspoon salt in a small bowl. Pat the mixture onto both sides of each pork chop. Place flour in a shallow dish; dredge each chop in the flour, shaking off any excess.
Heat oil in a large skillet over medium-high heat. Add the chops, reduce heat to medium and cook until browned and just cooked through, 2 to 3 minutes per side. Transfer to a plate and tent with foil to keep warm.
Reduce heat to medium-low. Add shallot to the pan and cook, stirring, until softened, about 1 minute. Add brandy and cook, stirring and scraping up any browned bits, until most of the liquid has evaporated, 1 to 2 minutes. Remove from the heat; stir in sour cream and the remaining 1/4 teaspoon salt. Serve the pork chops with the sauce.