Heat oil in a large deep skillet (preferably cast iron) over medium high heat. Sean the chops with salt and pepper and add to the skillet, browning well, about 3-4 minutes per side. Reduce heat if the chops are browning too quickly.
Remove the chops to a plate and pour off all but 2 tablespoons of fat. Add the flour and cook, whisking continuously, until a caramel colored roux is made.
Add the diced shallots and cook for an additional 2 minutes.
Add the mushrooms and cook until softened and then add the thyme.
Slowly whisk in the heavy cream. Add the Dijon mustard and simmer until thickened, about 5 minutes.
Add in a pat of butter to make the sauce smooth and glossy.
Serve the sauce immediately over the pork chops, garnished with fresh parsley.