Prep the chicken: Butterfly or slice thick breasts horizontally and gently pound each piece to an even thickness of about ½ inch. Pat dry, then season both sides lightly with kosher salt and pepper.
Set up dredging station: Place flour in one shallow dish. Whisk eggs with milk in a second dish. In a third dish combine panko, ¾ cup grated Parmesan, garlic powder, onion powder, and Italian seasoning.
Bread the chicken: Dredge a breast in flour and shake off excess. Dip into egg wash, then press firmly into the panko-Parmesan mix so crumbs adhere. Shake off any loose crumbs. For extra-crunch, double-dip (egg → crumbs again). Place breaded pieces on a wire rack and chill in the fridge 10–15 minutes to help adhesion.
Preheat oven and pan: Heat oven to 400°F (200°C). Warm a large heavy skillet (cast iron preferred) over medium-high heat with 3 tbsp neutral oil and 1 tbsp butter (optional) until shimmering.
Sear the chicken: Working in batches if needed, place breaded chicken into hot oil. Sear 3–4 minutes per side until deep golden brown. Don’t overcrowd. Transfer seared breasts to an oven-safe tray.
Finish in the oven: Bake the seared chicken in the preheated oven 6–10 minutes, or until an instant-read thermometer inserted into the thickest part reads ~160°F (71°C) — it will rise to 165°F (74°C) while resting. Remove and rest 3–5 minutes.
Make the Parmesan pan sauce: Using the same skillet over medium heat, add 2 tbsp butter. Sauté minced garlic 30–45 seconds until fragrant. Deglaze with white wine, scraping up browned bits; simmer until reduced by half (about 2 minutes). Add chicken stock and simmer 1–2 minutes. Stir in heavy cream and Dijon mustard, simmer 2–3 minutes until slightly thickened. Remove from heat and whisk in ¼–½ cup grated Parmesan until smooth. Add lemon juice and adjust salt/pepper to taste. If sauce is too thick, thin with a splash of stock.
Plate and serve: Place rested chicken on plates, spoon warm Parmesan sauce over the top, sprinkle with extra grated Parmesan and chopped parsley. Serve with lemon wedges if desired.