Preheat oven to 300 degrees F. Evenly spread bread cubes out on two baking sheets and bake for 15 minutes, or until bread is dried but not browned. Transfer bread cubes to a large bowl.
Meanwhile, in a large skillet, heat butter over medium-high heat. Add onion, celery, mushrooms, and apples. Cook until vegetables and apples are soft, about 10 minutes. Add the mixture to the bread and stir to combine.
In a medium bowl, whisk together the vegetable broth and two eggs. Pour the broth mixture over the bread and stir to combine. Make sure all of the bread cubes are well coated with the liquid. Season with sage, salt, and pepper and stir well.
Pour stuffing into a greased 9 x 13 pan. Bake at 350 degrees F for about 45 minutes, or until the stuffing is lightly browned and crisp on top. Remove from the oven and serve warm.