Preheat the oven to 400 degrees F and line a baking sheet with foil. Season the pork chops with salt and pepper. Heat 1 tablespoon vegetable oil in a large nonstick skillet over medium-high heat. Add the pork chops and sear until golden brown, 2 to 3 minutes per side. Transfer to the prepared baking sheet (reserve the skillet).
Mix the parmesan, oregano, lemon zest and garlic in a small bowl. Sprinkle on the pork chops. Bake until just cooked through, about 5 minutes. Remove from the oven and let rest 5 minutes.
Meanwhile, add the figs and 3 tablespoons water to the reserved skillet. Cook over medium-low heat until the figs are soft and most of the water has evaporated, about 2 minutes; season with salt and pepper. Transfer to a large bowl and add the arugula, fennel, croutons, the remaining 1 tablespoon vegetable oil and the lemon juice; toss. Serve with the pork.