4 scallions, white and tender green parts, thinly sliced
1/2 cup frozen baby peas, thawed
Preheat the oven to 400°. Season the pork chops on both sides with salt. Brush each chop with 1 teaspoon of the mustard; generously sprinkle all over with coarsely ground black pepper.
In a large skillet, heat 2 tablespoons of the olive oil until shimmering. Add the pork chops and cook over moderate heat, turning once, until golden, about 6 minutes. Transfer the chops to a baking sheet and roast for 12 minutes, until cooked through; keep warm.
Meanwhile, pour off the fat from the skillet. Add 1/4 cup of water and cook over high heat for 1 minute, scraping up any browned bits from the bottom of the pan. Pour the pan juices into a cup and wipe out the skillet.
Heat 2 tablespoons of the olive oil in the skillet. Add all but 1 tablespoon of the shallots and cook over moderately high heat until softened, 3 minutes. Add the vinegar and cook until nearly evaporated, about 30 seconds. Add the wine and cook until nearly evaporated, about 2 minutes. Add the cream and cook over moderately high heat until slightly reduced, about 2 minutes. Add the remaining 4 teaspoons of mustard, the reserved pan juices and half of the parsley. Season the sauce with salt and finely ground black pepper; keep warm.
Heat the remaining 2 tablespoons of olive oil in another large skillet. Add the sugar snaps, mushrooms, scallions and the reserved 1 tablespoon of shallots and cook over moderately high heat until the sugar snaps are crisp-tender and the mushrooms are tender and lightly browned, about 5 minutes. Stir in the peas and the remaining parsley and season with salt and finely ground pepper. Pour the cream sauce onto plates and top with the pork chops. Spoon the vegetables alongside and serve.