Preheat the oven to 375 degrees F. Slice the chicken breasts open lengthwise like a book, leaving them attached on one side. Sprinkle all over with 1 teaspoon salt, some pepper and the poultry seasoning.
Mash the pot pie in a medium bowl. Stir in the Cheddar and 2 tablespoons of the parsley. Spread the filling on one side of the open chicken breasts and fold closed. Place some flour in a shallow bowl and dredge the chicken on both sides.
Heat the oil in a large ovenproof skillet over medium-high heat. Carefully lay the stuffed chicken breasts in the skillet, cooking until brown on both sides, 2 to 3 minutes per side. Place the skillet in the oven and bake until the filling is bubbly on the edges and the chicken is completely cooked through, about 18 minutes more.
Remove the chicken to warm plates and keep warm. Return the skillet with the drippings to the stovetop over medium heat and sprinkle in the 2 teaspoons flour, stirring to incorporate. Add the chicken broth and scrape up the browned bits from the bottom of the pan to incorporate them into the sauce. Boil over high heat until reduced by half, 2 to 3 minutes. Reduce the heat, add the lemon juice and return to a simmer. Whisk in the butter, at piece at a time, to make a smooth sauce. Stir in the remaining 2 tablespoons parsley, spoon the sauce over the chicken and serve.