Cut the fennel. Preheat oven to 350F. Cut the stems and fronds off the fennel (reserve ¼ cup of the fronds), then discard any bruised outer layers. Cut the fennel bulb in half lengthwise, then using a paring knife cut out the tough part of the core (you essentially cut a small triangle shape to remove). Thinly slice the fennel into ¼" thick half moons, then place in a bowl of ice water.
Set up the breading stations with 3 pans. In a small, shallow container or bowl, combine 1 cup AP flour with 1 Tbsp Kosher salt and 1 tsp freshly ground black pepper. In the second pan, whisk 3 eggs. In the final pan or container, combine 1½ cups panko, ½ cup grated Parmesan, 2 Tbsp chopped sage, and remaining 1 Tbsp Kosher salt.
Preheat oil. Heat a few tablespoons of olive or vegetable oil over medium-high heat in a large skillet. The amount of oil will depend on the size of the pan you use -- you need an even layer on the bottom of the pan that goes up approximately ⅛" - ¼" up the side.
Dredge cutlets in flour. Place cutlets one at a time in the flour mixture, coating on both sides, then shaking off any excess flour. Move chicken to the eggs, turning to coat on all sides, allowing any excess to drip off. Finally, transfer the cutlets to the panko breadcrumbs, being sure to evenly coat on all sides.
Pan fry the cutlets. When the oil is hot, carefully place breaded chicken in the oil (working in batches, as needed) and cook for 3-4 minutes per side, until golden brown, but not burned.
Finish in the oven. Move pan to the oven and bake for 6-8 minutes, or until chicken is fully cooked through. Chicken is safe to eat at 165F, but you can remove it from the oven when it’s reached ~155F — it will continue to cook while it rests. If you're cooking more chicken cutlets than will fit in the skillet, transfer to a wire rack on top of a baking sheet, then finish in the oven.
Make the salad. While chicken is resting, drain the fennel, then add to a large mixing bowl with salad greens and 1-2 Tbsp high quality olive oil. Season to taste with Kosher salt and black pepper, then toss well.
Finish and serve. Plate the chicken cutlets, then sprinkle each with a pinch of flaky sea salt. Mound the fennel salad atop chicken, then garnish with reserved fennel fronds. Serve immediately with lemon wedges.