Heat oven to 275°F and adjust oven racks to upper-middle and lower-middle positions. Butter a 3-qt baking dish; set aside.
Divide bread evenly between 2 rimmed baking sheets and place on the oven racks. Bake, stirring occasionally, for 40-45 minutes or until bread is dried out but not browned. Transfer bread to a large bowl to cool completely.
Increase the oven temperature to 350°F and adjust oven rack to middle position.
While the bread bakes, heat a large skillet over medium heat and add the sausage. Break the sausage into bite-size pieces during cooking. Cook the sausage, stirring often, 6-8 minutes or until brown throughout.
Transfer cooked sausage to a paper towel-lined plate, and discard all except 1 tablespoon rendered fat from the skillet.
Reduce heat to medium-low and melt ¾ cup butter in the same skillet. Add diced onion, fennel, celery, carrots, and apple; mix well. Season with salt and pepper; stir well. Cook, stirring often, until vegetables and apple are tender, about 10-15 minutes. If the vegetables are browning, reduce the heat to low and continue cooking until softened.
Deglaze the pan with 1½ cups chicken stock and stir in parsley, sage and thyme.
When the bread has cooled, transfer it to a large bowl. Add the cooked sausage and the vegetable/apple mixture; gently mix.
In a small bowl, whisk together the remaining 1½ cups broth and eggs. Pour the egg mixture over the bread mixture and fold gently until well combined.
Let the mixture sit, stirring occasionally, about 10 minutes or until bread absorbs all liquid.
Transfer mixture to the prepared baking dish. Butter (or spray with nonstick spray) one side of a sheet of foil and cover the dish with the foil, greased side down.
Set the dish on the middle rack and bake, covered, 35-40 minutes or until very hot to the touch. The internal temperature (tested in the middle) should register 160°F on an instant-read thermometer.
Remove the foil and bake an additional 30-45 minutes or until the stuffing is set in the middle and the top is golden brown.
If the stuffing needs more browning after fully cooked, turn the broiler on and cook until the top has browned to your liking. Watch closely.
Transfer to a cooling rack and allow to cool 5-10 minutes before serving.