Dry pork and sprinkle both sides with the salt and pepper. In a saute pan or skillet, heat the oil and butter to almost smoking. Add the pork and brown well, about two minutes per side. Remove.
Add the shallots to the pan and saute until golden. Add the mushrooms and saute until beginning to color. Add the thyme and return the pork chops to the pan. Reduce heat to medium, cover, and cook until pork is just cooked through, about 5 minutes longer. Do not overcook.
Remove the pork to a warm serving platter. Raise heat and add Madeira. Bring to boil, stirring and scraping pan, and cook until reduced to half.
Add cream, bring to a boil and cook, stirring constantly until lightly thickened. Pour sauce over pork, sprinkle with parsley and serve.