Preheat oven to 425°F. Line a large rimmed baking sheet with heavy gauge aluminum foil.
Toss your washed and quartered pears with 1 tablespoon of the olive oil. Add 1/4 teaspoon each Kosher salt and black pepper and toss again. Turn the pears out onto the prepared baking sheet. Arrange so that all of the cut sides are facing up. Roast the pears for 10 minutes. While the pears are roasting, fry the pork chops.
In a large cast iron skillet, heat the remaining tablespoon of olive oil with the butter over medium heat until shimmering. Season each pork chop which you have patted dry with 1/2 teaspoon each Kosher salt and black pepper being sure to coat all sides.
Fry the chops until golden brown on both sides, about 3 minutes per side each. Remove the cast iron from the heat. Remove the pears from the oven. Place side by side.
Toss the partially roasted pears with the maple syrup. Transfer the partially cooked chops to the baking sheet being sure to nestle in and among the pears and somewhat flat in the syrup against the baking sheet. Do NOT discard the pan juices in the skillet.
Place the baking sheet with the chops and the pears back into the oven for an additional 5 to 7 minutes. Chops will read 145°F on an instant read thermometer when they are cooked. Pears should be golden brown and tender. While the chops and pears finish in the oven, prepare the pan sauce.
Return the skillet with the pan juices to medium heat and add the garlic. Cook, stirring, for 1 minute. Add the wine and reduce by half. Remove the skillet from the heat and whisk in the mustard and the finely minced parsley.
Once the chops reach 145°F, transfer to a platter. If using walnuts, toss them now with the pears and the juices while still on the baking sheet. Spoon the pear mixture over the chops and drizzle the pan sauce over top all.