Season the pork chops generously with salt and pepper. Dredge in the flour and shake off any excess.
Pour oil into a large skillet to a depth of 1/8 of an inch and heat over high heat until the surface of the oil is shimmering but not smoking. Add the pork chops and pan-fry them on one side until golden brown, 3 to 4 minutes. Turn carefully the chops over and continue cooking on the second side until the chops are cooked through and the exterior is golden brown. Transfer them to a warm place and cover with aluminum foil to keep warm.
Pour off all the fat except 2 tablespoons of the oil. Add the shallots to the skillet and sauté over medium heat until translucent, about 1 minute. Increase the heat to high and add the mushrooms and thyme and sauté until the mushrooms are lightly brown, 3-4 minutes.
Add the wine and stir to deglaze the pan, scraping up any browned bits from the bottom. Add the broth and any juices released from the chops. Simmer over high heat until the liquid has reduced by about half, 5 to 7 minutes.
Swirl in the butter to thicken the sauce slightly. Serve the pork chops immediately with the sauce.