Prepare the dredging station: Whisk the egg in a shallow bowl. In a separate bowl, mix panko breadcrumbs, parmesan cheese, 0.5 teaspoon salt, and 0.25 teaspoon pepper.
Coat the zucchini: Dip each zucchini round into the egg, then press into the panko mixture until fully coated.
Fry zucchini: Heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Fry zucchini rounds in batches for 3 minutes per side until golden brown. Remove and drain on a wire rack.
Prepare chicken: Season chicken cutlets with remaining salt and pepper, then dredge lightly in flour, shaking off excess.
Sear chicken: Wipe the skillet clean. Melt 2 tablespoons of butter with the remaining 1 tablespoon of olive oil. Sear chicken for 5-6 minutes per side until internal temperature reaches 165F. Remove chicken from the pan.
Create sauce base: Add remaining 2 tablespoons of butter to the skillet. Sauté minced garlic for 60 seconds until fragrant.
Deglaze: Pour in chicken stock, scraping the bottom of the pan to release fond. Simmer for 3 minutes until liquid reduces by half.
Finish sauce: Stir in heavy cream, lemon juice, and lemon zest. Simmer for 2-4 minutes until the sauce achieves a coating consistency.
Combine and serve: Return chicken cutlets to the pan to coat with sauce. Serve immediately with the crispy zucchini rounds.