Preheat a large saute pan over medium heat, add 2 tablespoons butter and allow to melt. When the butter is melted and bubbling, add the chopped apple. Stir in the lemon juice and honey with a spatula to coat the apples. Continue to cook until the apples are golden, stirring occasionally, 10 to 15 minutes. (If the apples get too brown, remove from the heat and set aside).

In another large saute pan over medium-high heat, add 2 tablespoons butter and allow to melt. While the butter melts, mix together the flour, 2 teaspoons salt and the pepper in a large bowl. Dredge the chicken breasts in the flour mixture until thoroughly coated. Carefully place the dredged chicken into the heated pan and brown on each side, about 5 minutes per side. Remove the chicken breasts to a baking sheet or oven-safe warming plate and cover with foil. Set aside.

In the same saute pan, add the chicken stock and apple and cranberry juices to deglaze the pan. Add the cinnamon stick. Add the remaining 1 teaspoon salt to the mixture, whisking to combine. Allow the sauce to reduce until it reaches a nice thick brown gravy consistency, 35 to 40 minutes. Remove the cinnamon stick.

Add the cooked apples to the thickened sauce and whisk in the remaining 2 tablespoons butter. Add the cooked chicken breasts to the apples and gravy, to reheat briefly (about 1 minute). Plate the chicken breasts, top with the apples and sauce and sprinkle with the parsley.