Sprinkle the pork with 1 tsp. salt and 1/2 tsp. black pepper. Put the flour in a small bowl, and then dredge the pork in the flour, shaking off any excess.
Heat 1 Tbs. oil and the butter in a large (12-inch) heavy-duty skillet over medium heat until the butter melts. Add the pork and cook, without touching, until it starts to brown nicely and easily releases from the pan, about 4 minutes. Flip and cook the other sides in the same manner until the pork is cooked through and then transfer to a large serving platter. Cover loosely with foil.
To make the sauce, add the remaining 1 Tbs. oil and shallot to the pan, sprinkle with 1/4 tsp. salt, and cook, stirring, until the shallot softens and becomes translucent, about 2 minutes. Add the mushrooms and cook, stirring, for 1 minute. Add the Marsala, raise the heat to high, and cook, scraping the bottom of the pan with a wooden spoon to loosen any browned bits, until the liquid has almost completely reduced, about 2 minutes. Stir in the mushroom soaking liquid and cook until it reduces by about half, about 4 minutes. Whisk in the cream and bring to a boil. Take the sauce off the heat and spoon it over the pork. Serve sprinkled with parsley.