Season chicken cutlets with salt and pepper, then dredge in 0.25 cup of flour.
In a large skillet, heat 1 tablespoon olive oil and 1 tablespoon butter over medium-high heat.
Sear chicken for 5-6 minutes per side until golden and internal temperature reaches 165°F (74°C). Remove and set aside.
In a shallow bowl, combine panko and parmesan. Dip zucchini rounds into beaten egg, then press into the panko mixture.
Heat 2 tablespoons olive oil in a separate skillet over medium heat. Fry zucchini rounds for 3 minutes per side until crispy. Drain on paper towels.
In the chicken skillet, melt 1 tablespoon butter and sauté minced garlic for 60 seconds.
Pour in chicken broth to deglaze the pan, scraping the bottom with a wooden spoon. Simmer until liquid is reduced by half.
Reduce heat to medium-low and whisk in heavy cream and lemon juice. Simmer for 3-5 minutes until thickened.
Stir in the remaining butter, lemon zest, and parsley.
Return chicken to the skillet to coat with sauce. Serve immediately alongside the crispy zucchini rounds.