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Preheat the oven to 400°. Season the pork chops generously with salt and pepper and let stand at room temperature for 30 minutes.
In a shallow bowl, whisk 1/2 cup of the flour with the dry mustard, 1 teaspoon of the smoked paprika, 1 tablespoon of salt and 2 teaspoons of pepper. Working one at a time, dredge the pork chops in the seasoned flour and gently shake off the excess. Transfer to a large plate.
In a large skillet, heat 2 tablespoons of the oil until shimmering. Add 2 of the pork chops and cook over moderately high heat, turning once, until browned, about 3 minutes per side. Using tongs, transfer the pork chops to a rack set in a rimmed baking sheet. Repeat with the remaining pork chops. Transfer the chops to the oven and bake for about 8 minutes, until an instant-read thermometer inserted into the thickest part reads 135°. Tent the chops with foil.
While the chops bake, wipe out the skillet and heat the remaining 2 tablespoons of oil until shimmering. Add the mushrooms, onion, garlic and to the skillet and season with salt and pepper. Cook over moderate heat until tender, stirring occasionally, about 10 minutes. Transfer the vegetables to a medium bowl. Wipe out the skillet.
In the same skillet, melt the butter over moderate heat. Add the remaining 3 tablespoons of flour, whisking constantly, and cook for 1 minute, until smooth. Add the broth and whisk until no lumps remain. Return the mushrooms to the skillet and simmer over moderate heat until the sauce is thick enough to coat the back of a spoon, about 5 minutes. Add the cream, parsley and remaining 1 teaspoon of smoked paprika, and simmer over moderate heat for 2 minutes. Season the sauce with salt and pepper. Arrange the pork chops on a serving platter, spoon the mushroom sauce on top and serve.