Preheat the oven and prepare the chicken. Preheat your oven to 375°F. If needed, lightly pound the thickest sections of the chicken breasts so they are relatively even in thickness and cook evenly. You should have about three medium-sized chicken breasts weighing 2 pounds total.
Season the chicken. Combine the salt, pepper, garlic powder, thyme, sage, rosemary, and 3 tablespoons of olive oil in a medium-sized mixing bowl. Add the chicken breasts and toss until they're thoroughly coated with the herb mixture.
Prepare the stuffing. Place the dry stuffing mix in a large mixing bowl. In a separate bowl or large measuring cup, whisk together the chicken broth, eggs, and melted butter. Pour the mixture over the stuffing and stir thoroughly, making sure every piece of stuffing is moistened. Let the stuffing sit while you brown the chicken so it has time to absorb most of the liquid.
Heat the skillet. Add 1-2 tablespoons of olive oil to a 3.5-quart oven-safe skillet or braiser and heat over medium heat.
Brown the chicken. Once the oil is hot, add the chicken breasts and cook for 4-5 minutes per side, or until both sides are nicely browned. The chicken does not need to be cooked through at this point. Turn off the heat and remove the chicken from the skillet.
Grease the pan. If needed, use a paper towel to carefully spread the remaining oil in the pan across the bottom and up the sides. This helps prevent the stuffing from sticking.
Add the stuffing to the skillet. Pour the prepared stuffing into the same skillet, leaving the browned bits from the chicken in the pan. Spread the stuffing into an even layer.
Top with the chicken. Arrange the browned chicken breasts on top of the stuffing, keeping them in a single layer.
Bake the chicken and stuffing. Bake uncovered at 375°F for about 35 minutes, or until the chicken reaches 165°F in the thickest part and the stuffing is cooked through.
Rest and serve. Let the chicken and stuffing rest for 5-10 minutes before slicing the chicken and serving. Enjoy!