Preheat your oven to 375°F (190°C). Prepare a 9x13-inch baking dish by spraying it with cooking spray to prevent sticking.
If you are using boxed stuffing, follow the package instructions. For fresh stuffing, cube the stale French bread and let it sit out overnight to dry and harden.
In a large skillet, melt the unsalted butter over medium-high heat. Add the chopped onions and diced celery, sautéing until they soften, about 5 minutes. Stir in the minced garlic, Italian seasoning, and thyme, cooking for another minute.
Combine the stale bread cubes with the sautéed vegetables in the skillet. Drizzle in the chicken broth and mix in the grated Parmesan and minced parsley. Set the stuffing aside to cool slightly.
Slice each chicken breast lengthwise to create a pocket, being careful not to cut all the way through. Generously stuff each pocket with the prepared stuffing mixture.
Drizzle the stuffed chicken breasts with olive oil and season with Italian seasoning, garlic powder, paprika, salt, and freshly ground black pepper.
Place the stuffed chicken in the prepared baking dish and cover it with foil. Bake in the preheated oven for 25 minutes. After that, uncover and bake for an additional 12 to 15 minutes until the internal temperature reaches 165°F (74°C).
For a crispy top, you may broil the chicken for 1 to 3 minutes at the end of baking. Allow the chicken to rest for a few minutes before slicing and serving.