Pat the pork chops dry with paper towels. Season all over with the salt and pepper.

Heat the olive oil in a large, heavy bottom skillet over high heat. Once the oil just begins smoking, working in batches, add the pork chops. Cook, undisturbed, for 3 minutes, then flip and continue cooking for another 3 minutes. Continue cooking this way, flipping the pork, until the internal temperature of the pork reads 160°F, 15 minutes total. Transfer the pork chops to a serving platter and cover with foil to keep warm. Repeat with remaining pork chops.

Reduce the heat to medium and add the butter to the pan. Once the butter melts, add the mushrooms and stir until softened and browned, about 5 minutes. Add the garlic and cook for 1 more minute. Stir in the wine and thyme, then bring to a simmer. Cook until the liquid is reduced by about half, 5 minutes. Stir in the heavy cream and mustard until combined, simmer until the sauce is thick enough to coat the back of a wooden spoon, about 4 more minutes. Taste and season with salt and pepper.

Return the pork to the skillet, spooning them with the sauce to coat. Squeeze fresh lemon juice over top and garnish with the chives. Divide among 4 plates.