Prepare the pork- Combine the brown sugar, paprika, coriander, onion powder, garlic powder, mustard powder, 1 tablespoon salt and 1/4 teaspoon pepper in a large baking dish. Pierce both sides of the pork chops with a paring knife (about 12 times per side). Add the pork chops to the dish, turning to coat with the spice rub. Cover and refrigerate at least 4 hours or overnight.
Make the sauce- Combine the vinegar, preserves, garlic, Worcestershire sauce, mustard powder, red pepper flakes and 3/4 teaspoon salt in a medium saucepan. Bring to a boil, then reduce the heat to medium low and simmer, whisking occasionally, until the sauce thickens slightly, about 8 minutes; let cool completely. Transfer 1/4 cup of the sauce to a separate bowl for basting. Set aside the remaining sauce for serving.
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Remove the pork from the refrigerator about 30 minutes before grilling. Preheat a grill to medium and lightly brush the grates with vegetable oil. Transfer the pork chops to the grill, cover and cook until lightly marked, about 4 minutes. Flip the pork chops and baste with the sauce; cover and cook 3 more minutes. Uncover and continue cooking, flipping and basting the pork chops every 2 minutes, until they are golden and well marked, about 8 more minutes. Transfer to a cutting board and let rest 5 minutes.
Meanwhile, brush the peaches lightly with vegetable oil and place cut-side down on the grill. Cover and grill until marked, 1 to 2 minutes per side. Serve the pork chops with the grilled peaches and the reserved sauce.
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