Preheat the oven to 375°F. Using a sharp knife, cut a pocket the length of each turkey tenderloin, being careful not to slice through all the way. Place the tenderloins, cavity side up, in a small baking dish that's been coated with cooking spray. Season lightly with salt and pepper and set aside.
Place the bread cubes* in a colander and moisten with water. Using your hands, squeeze out the water (as you would a sponge). Place the moistened bread in a mixing bowl and add the salt, pepper, egg, sage, thyme and parsley. Combine thoroughly and set aside.
Melt the butter in a skillet over medium heat and add the onion and celery. Season with a pinch of salt and pepper and sauté until the onion is soft and translucent, 3 to 4 minutes. Remove from the heat and allow to cool for 5 minutes, then add to the bread mixture and combine well.
Spoon the stuffing into the turkey tenderloins, mounding it slightly.**
Cover the dish loosely with foil, bake for 30 minutes, then remove the foil and bake for an additional 10 to 15 minutes, or until the stuffing is lightly browned and the turkey has reached an internal temperature of 165°F. Allow to rest for 5 minutes before.
While the turkey is baking, heat the butter in a large skillet over medium heat. Add the mushrooms and cook until any liquid they give off has evaporated and they are starting to brown, 5 to 7 minutes. Season with salt and pepper, then add 2 cups of the chicken broth and bring to a simmer.
In a small bowl, whisk together the flour and the remaining 1/4 cup of chicken broth. Add the mixture to the mushrooms gradually and stir until well blended. Simmer until the gravy is thickened, 2 to 3 minutes longer. Cover and keep warm.
Plate individual servings of turkey, top with mushroom gravy and serve alongside mashed sweet potatoes and oven-roasted brussels sprouts (see below).
Tips for Making This Recipe
*Choose a soft bread with a dense texture and relatively tender crust for your stuffing. We like sourdough, but Italian bread works well too.**You can spoon any leftover stuffing into the baking dish between the tenderloins or bake in a separate dish if desired.