Prepare a grill for medium-high heat. Sprinkle the pork chops generously on both sides with salt and pepper. Lightly oil the grill grates. Grill the pork chops until lightly charred with strong grill marks, about 6 minutes. Flip and continue to grill until just slightly pink near the bone, 4 to 5 minutes more. Transfer the pork chops to a cutting board to rest for about 5 minutes.
Meanwhile, toss the plums with 2 teaspoons of the oil and sprinkle with salt and pepper. Grill, flipping once, until softened with grill marks, about 2 minutes per side. Cut into wedges.
Toss the arugula and parsley with the lemon juice and remaining 1 tablespoon oil and season with salt and pepper. Divide among 4 plates and top with the plum wedges. Serve with the pork chops.
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