Spoon pesto into a separate bowl and slice the cheese into thin slices. Separate bacon slices and place everything on a work station.
Lay the chicken breast flat on the cutting board. Carefully, slide the knife (hold it sideways with blade facing away from you) at the top (larger part) of the chicken breast in the center and cut a pocket in the middle. DO NOT slice all the way through the bottom or the sides of the chicken breast. Your ultimate goal is to create a pocket inside the breast with opening at the top. Repeat with all four breasts.
Using your hands, add about a tablespoon of pesto inside each chicken breast pocket.
Stuff the chicken with 3-4 slices of cheese each. Make sure the cheese is even throughout the chicken pocket. Close the opening of the chicken with a toothpick.
Salt each stuffed chicken breast.
Wrap each chicken breast with two slices of bacon, tucking the ends under one of the bacon rings.
Preheat oven to 350 and preheat a cast iron skillet (or a cooking pan that is oven safe) on stove-top, over medium-high heat. Make sure that your skillet is well seasoned and lightly greased. (If using an oven-safe cooking pan, you'll want to use a couple of tablespoons of oil to grease the pan.)
Carefully place each chicken breast in the hot skillet. Sear chicken for about 3 minutes on each side. Your goal is to sear the bacon, not to cook the chicken all the way.
(Carefully pour off most of the bacon grease.)
Transfer the skillet into pre-heated oven and bake for about 15 minutes.
(Judge cooking time according to the size of the biggest thicken breast.)