Place chicken breasts between two sheets of plastic wrap and pound to an even 1/2-inch thickness using a meat mallet or rolling pin. Pat dry and season both sides with salt and pepper.

Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Once the butter is melted and foaming, add the chicken in a single layer. Cook for 5-6 minutes per side until deeply golden and internal temperature reaches 165°F. Transfer to a plate and tent with foil.

Reduce heat to medium. Add the remaining 1 tablespoon butter and garlic to the skillet; sauté 30 seconds until fragrant. Pour in chicken broth, scraping up browned bits with a wooden spoon. Bring to a simmer and cook until reduced by half, about 3-4 minutes.

Stir in heavy cream, lemon juice, and lemon zest. Simmer for 2 minutes until slightly thickened. Whisk in Parmesan cheese until melted and smooth. Season with extra salt and pepper to taste.

Return chicken to the skillet, spooning sauce over the top. Simmer for 1-2 minutes to warm through. Garnish with parsley and additional lemon slices. Serve immediately.