Preheat oven to 350 F.
Cut the tenderloins into 2" rounds. Flatten slightly and season with salt and pepper.
Heat the oil and one tablespoon of the butter in a large oven-proof skillet (I prefer to use cast iron for this). Get the oil as hot as possible without smoking.
Add the pork and sear on both sides, 2-3 minutes per side. Remove to a plate.
Reduce heat to medium and add the remaining butter to the skillet. Melt.
Add the shallot and a pinch of salt and saute for 30 seconds. Use a flat spatula (a wooden spoon works great) to scrape up any yummy bits stuck to the bottom of the pan.
Add the mushrooms and saute until golden brown and the moisture is released and evaporated, 5-7 minutes.
Sprinkle with salt and the flour.
Slowly stir in the Marsala until it is nearly evaporated.
Stir in the chicken broth. Reduce heat to a simmer and let simmer until reduced by half.
Stir in the cream and parsley. Add the pork and any accumulated juices back to the pan.
Place in the oven and cook until the internal temperature reaches 155-165 F.
Season with salt and pepper.
Serve pork with plenty of the gravy and mushrooms.