Combine panko, grated parmesan, 1/4 tsp. salt, and 1/4 tsp. pepper on a large plate. In a small bowl, lightly beat eggs. Dip each pork chop in egg, then transfer to panko mixture and coat completely with crumbs. Set aside.
In a large bowl, combine arugula, fennel slices, and parmesan shavings. Drizzle salad with 3 tbsp. olive oil and the lemon juice. Toss, season with remaining salt and pepper, and toss again.
In a 12-in. nonstick frying pan, heat remaining 1/2 cup olive oil over medium-high heat. Add two pork chops and cook, turning once, until crusts are deep golden brown and crisp, 5 to 6 minutes. Transfer chops to a plate and keep warm. Repeat with remaining chops.
Cut each chop in half diagonally and arrange on a serving platter with salad. Serve immediately.
Note: Nutritional analysis is per serving.