In a large (10- to 12-inch) cast-iron skillet, melt 1 1/2 tbsp. butter over medium-high heat. Add the mushrooms; cook, stirring, until browned, 6 to 7 minutes. Transfer the mushrooms and juices to a plate.
Pat the pork dry; season with 1 tsp. salt and 1/2 tsp. pepper. Add to the skillet and cook, turning once, until the pork is browned on both sides and firm to the touch, about 8 minutes. Transfer the pork to plates; tent with foil to keep warm.
Add the shallot to the skillet and cook, scraping up any browned bits, until softened, 1 to 2 minutes. Stir in the wine; boil until reduced by half, about 2 minutes. Stir in the beef broth; boil until thickened slightly, about 2 minutes. Stir in the mustard, thyme and remaining 1 1/2 tbsp. butter until melted. Add the mushrooms back to the pan, turn off the heat and let sit until heated through, about 1 minute; season with salt and pepper. Return the pork chops to the skillet and serve.