Melt 2 T butter in an oven-proof skillet over medium heat. Add mushrooms and saute until soft and lightly browned, about 6 minutes. Remove from pan and set aside.
Melt remaining butter in the same skillet over low heat. Add shallot and saute gently until soft, about 8-10 minutes. Remove from pan and set aside.
Season pork chops with salt and pepper. Heat the same skillet over medium-high heat and sear pork chops on one side, about 2 minutes. Turn and sear the other side, roughly the same time. Remove from heat and set aside.
Return the same skillet to medium heat. Deglaze the pan with chicken broth, scraping bits from the bottom. Whisk in cream, thyme leaves, mustard and worschestershire. Simmer until well incorporated and slightly thickened, about 5 minutes. Stir in mushrooms and shallots. Return pork chops and juices to the pan. Spoon the sauce over the chops and turn off the burner.
Place the skillet in the preheated oven and finish for 20-35 minutes, depending on the thickness of the pork.