In a small bowl, combine the remaining 2 teaspoons of salt, 2 teaspoons of pepper, and the lemon zest. Rub the lemon-pepper mixture evenly on all sides of the chicken.

Dredge the chicken in flour mixture to coat. Set chicken aside.

Thinly slice one of the lemons, set them all aside.

Heat 2 tablespoons of butter and 2 tablespoons of olive oil in a large skillet over medium-high heat until bubbly.

Working in batches, add the chicken to the skillet. Cook until the chicken is browned on both sides, about 4 to 6 minutes per side. Add the remaining 2 tablespoons olive oil in between batches, if needed.

Transfer the chicken to a serving platter and tent with foil to keep warm.

Reduce the heat to medium and add the remaining 2 tablespoons of butter and the reserved 1 tablespoon of the flour mixture to the skillet. Cook, stirring constantly, until the flour is toasted, about 1 minute.

Add the garlic, lemon slices and the chicken broth to the skillet. Cook, stirring occasionally, until the sauce is bubbling and slightly thickened, and the garlic is lightly browned, 2 to 3 minutes.

Spoon the sauce and sliced lemons over the chicken. Garnish with parsley and serve with lemon wedges, if you like.