Pound out the pork chops. Place pork chops between two sheets of plastic wrap or parchment paper, then use a meat mallet or rolling pin to pound them to an even thickness of about ¼ inch.
Cut the fennel. Preheat an oven to 350°F (177°C). Trim fennel by removing stems and fronts (reserve ¼ cup), then discard any tough outer layers. Halve the bulb, remove the core with a paring knife, then thinly slice into ¼-inch half moons. Place in ice water.
Setup 3 shallow pans for breading. In the first, mix ½ cup all-purpose flour with 1 tsp kosher salt and ¼ tsp black pepper. In the second, whisk 2 eggs. In the third, combine 1 cup panko breadcrumbs, ¼ cup grated Parmesan, 1 Tbsp chopped sage, and ½ tsp kosher salt.
Heat oil. Heat a few tablespoons of olive or vegetable oil in a large skillet over medium-high heat. Use enough oil to coat the bottom in an even layer, about ⅛ inch - ¼ inch deep, depending on the size of your pan.
Dredge the cutlets. Dredge each cutlet in the flour mixture, coating both sides and shaking off excess. Dip into the eggs, turning to coat, then let excess drip off. Press into the panko-mixture, ensuring all sides are well coated.
Pan fry the cutlets in hot oil, working in batches if needed. Cook for 3-4 minutes per side, until golden brown but not burned.
Finish in the oven for 6-8 minutes, or until fully cooked through. The pork should reach an internal temperature of 145°F (63°C), but remember the temperature will continue to rise as it rests. If you’re cooking larger portions, transfer cutlets to a wire rack set over a baking sheet before baking.
Make the salad. Drain fennel, then toss with 2 cups arugula, ¼ cup shaved Parmesan, 2 Tbsp extra virgin olive oil, 1 tsp lemon zest, ½ tsp kosher salt, and a little black pepper in a mixing bowl.
Finish, then serve! Plate pork cutlets, sprinkle with flaky sea salt, then top generously with fennel salad. Garnish with a few of the reserved fennel fronds, then serve with lemon wedges.