Season both sides of chicken with salt and pepper.
Dredge both sides of chicken breasts in flour, one at a time.
Heat a skillet over medium-high heat. Add olive oil and 1 Tbsp butter, then sear chicken breasts until golden brown on both sides.
Transfer chicken to a plate. In the same skillet, sauté garlic, then pour in chicken broth and lemon juice. Simmer until liquid reduces by half.
Add remaining butter and lemon zest to the skillet. Return chicken to skillet, spoon sauce over chicken, and garnish with parsley.