Heat oven to 400° F. Heat 1 tablespoon of the oil in a large skillet over medium-high heat. Season the chops with ¾ teaspoon each salt and pepper.
Add 4 chops to the skillet and cook until browned, about 2 minutes per side. Transfer to a baking sheet. Repeat with the remaining chops.
Transfer the baking sheet to oven and roast chops to desired doneness, 4 to 6 minutes for medium-rare.
Meanwhile, in a medium bowl, combine the tomatoes, garlic, fennel, lemon juice, oregano, ¼ teaspoon each salt and pepper, and the remaining oil.
Divide the arugula and chops among individual plates and spoon the tomato mixture over the greens.