Preheat your oven or grill and set the temperature to 375°F.
While the oven or grill is preheating, mix together the room temperature cheeses, ¾ cup of spinach and the lemon zest in a medium sized mixing bowl. Set it aside.
Cut a pocket into the side of each chicken breast, being careful not to cut all the way through.
Stuff the pockets with equal portions of the cream cheese mixture, and lightly season the outside of the chicken with the barbecue rub.
Tightly wrap each stuffed chicken breast with bacon. Be sure to position the end of each slice on the bottom of the chicken breast. Lightly season the bacon wrapped stuffed chicken breasts, and place them in a baking dish or oven safe skillet.
Place the skillet inside the oven or grill. Let the chicken bake for about 30 minutes, until the internal temperature reaches 150°F as indicated by a reliable quick read thermometer.
Remove from the oven and set the chicken breasts on a cutting board to rest. Carry-over cooking will finish cooking the chicken through. Spoon out and discard all but one tablespoon of the rendered bacon fat, leaving any cheese that leaked out in the pan.
Place the pan on the stove over medium heat, and add the flour. Whisk the flour constantly for two minutes. Then, slowly add the chicken broth and continue whisking until the sauce is the consistency of syrup, about three minutes. Whisk in the remaining chopped spinach. Spoon a portion of the sauce on a plate, top with bacon wrapped stuffed chicken breast and garnish with chopped parsley.