Place flour in a shallow dish and season with salt and pepper. Place beaten eggs in a second dish. In a third dish, mix Panko, Parmesan, chopped parsley, and lemon zest.
Dredge each chicken cutlet in the flour, shaking off excess. Dip into the egg wash, then press firmly into the breadcrumb mixture to coat both sides evenly.
Heat olive oil and 1 tablespoon of butter in a large skillet over medium-high heat. Once shimmering, add chicken cutlets. Cook for 3-4 minutes per side until golden brown and crispy. Transfer chicken to a plate.
Reduce heat to medium. Add the remaining 2 tablespoons of butter and the minced garlic to the skillet. Sauté for 1 minute until fragrant.
Pour in the chicken broth and lemon juice, scraping up any browned bits from the bottom of the pan. Simmer for 2-3 minutes until the sauce reduces slightly.
To serve, place chicken cutlets over a bed of warm brown rice and drizzle the lemon butter sauce over the top. Garnish with extra parsley and lemon wedges.