Prepare the chicken: Place chicken cutlets between two sheets of plastic wrap. Pound them to an even 1/4-inch thickness. Season lightly with salt and pepper.
Set up the breading station: Place flour on one shallow plate. Beat eggs in a second shallow dish. Mix Panko breadcrumbs, grated Parmesan cheese, salt, pepper, and garlic powder on a third shallow plate.
Dredge each cutlet: Coat a cutlet first in flour, shaking off excess. Dip it completely into the egg wash. Press firmly into the Panko mixture to coat both sides thoroughly. Place coated cutlets on a wire rack.
Cook the chicken: Heat the vegetable oil in a large skillet over medium-high heat until shimmering (about 350°F). Carefully place 3 or 4 cutlets in the hot oil, ensuring not to overcrowd the pan. Fry for 2 to 3 minutes per side until golden brown and cooked through. Remove and drain on a clean wire rack or paper towels. Repeat with remaining cutlets.
Make the sauce: In the same skillet (drain off most of the oil, leaving about 1 teaspoon), melt the butter over medium heat. Add the minced shallot and cook until soft, about 2 minutes.
If using wine, pour it in and let it reduce by half, scraping up any browned bits from the bottom of the pan.
Pour in the heavy cream and lemon juice. Bring to a gentle simmer and cook for 3 to 5 minutes, stirring occasionally, until the sauce thickens enough to coat the back of a spoon. Season with salt and pepper to taste.
Stir in the fresh parsley.
Serve immediately: Arrange the crispy cutlets on plates. Spoon the lemon cream sauce over the top or serve the sauce on the side to maintain maximum crispiness.
Notes
For extra crispiness, chill the breaded cutlets for 15 minutes before frying.
If you prefer not to fry, you can bake the cutlets at 400°F for 15 to 18 minutes, flipping halfway through.
Do not add the sauce to the cutlets until you are ready to serve them to prevent the crust from becoming soggy.