• Preheat the oven to 375°F (190°C). Warm the olive oil and 2 tablespoons butter in a 10- or 12-inch oven safe skillet (preferably cast iron) over medium heat. Add the onion and celery and sauté for about 5 minutes, until softened. Stir in the stuffing mix, ½ cup broth, garlic powder, onion powder, thyme, and lemon juice. Stir until just moistened and remove from heat to cool slightly.
• Lay the chicken breasts flat and season both sides with salt and pepper. Add a few slices of cheese to each piece, followed by about ⅓-½ cup of stuffing, pressed a bit to help it hold together. Fold the chicken around the filling, pressing gently to seal, and secure with a toothpick at the seam. (Thread the toothpick like you might thread a safety pin through fabric.) Press any extra stuffing into the ends of the chicken rolls.
• Wipe out the skillet, melt 1 tablespoon butter over medium-high heat. Once melted and pan is hot, sear the stuffed chicken 2–3 minutes per side (top and bottom is good enough) until golden. Brush the tops with beaten egg, sprinkle evenly with panko, press slightly to help it adhere, and drizzle the remaining 2 tablespoons melted butter over the top.
• Transfer the skillet to the oven and bake uncovered for 25–30 minutes, or until the chicken reaches an internal temperature of 160°-165°F. (It will continue to cook while resting, so lean closer to the lower end for juicy, not dry chicken.)
• For the crispiest topping, remove pan from oven, shift the oven rack closer to the top (I set mine on the 2nd rung from the top), and turn the oven to broil. Return pan to oven for 1-2 minutes, watching closely so the topping browns without burning.
• Remove pan from oven, lightly cover with foil and let rest 5 minutes before serving. Finish with a light spritz of lemon juice and parsley for color and freshness. Remove toothpicks and serve!

Optional gravy:

• After broiling, transfer chicken and any large chunks of stuffing to a platter and cover lightly with foil. Add 2 tablespoons of butter to the remaining stuffing bits left in the pan and let it melt over medium heat. Whisk in the flour and cook for 30 seconds, scraping up any brown bits. (This is gold!)
• Slowly pour in the remaining broth from the can while whisking. Add cream. Simmer for 3-5 minutes until thickened. Taste and adjust seasoning with salt, pepper, and a small squeeze of lemon for brightness.