Remove chicken from packaging and dry with paper towels.
Add 1/2 cup flour, 1/2 teaspoon salt, and 1/2 teaspoon pepper to a 1-gallon resealable plastic bag. Add chicken, a few pieces at a time, and shake to coat, shaking off excess flour as you remove it from the bag.
In a 12-inch skillet, melt butter. Add the coated chicken pieces and cook over medium heat, 7-9 minutes per side or until chicken is cooked and an instant-read thermometer reads 170 degrees. Remove chicken to a plate and loosely cover with aluminum foil to keep it warm.
Add the chicken broth to the pan drippings. Bring to a boil over medium heat and stir well, lifting up any brown bits on the bottom of the pan. Reduce the heat and simmer, uncovered, about 8 minutes.
Add lemon slices, pushing them to the bottom of the skillet and continue simmering another few minutes or until the broth is reduced to about 1/3 of a cup. Remove the lemon slices to the plate of chicken.
Stir in 3/4 cup cream and the lemon juice and simmer over medium-low heat for about 5 minutes. Add remaining 1 tablespoon flour and remaining 1/4 cup cream to the skillet and whisk until smooth.
Bring sauce to a boil; cook for 1-2 minutes or until sauce has thickened.
Slip the chicken back in the sauce and flip it over once to coat. Garnish with caramelized lemon slices, lemon zest, and parsley as desired.