Once the cornbread has cooled enough to handle, crumble it onto a large baking sheet and scatter the sandwich bread cubes on top. Toast the bread in the oven for 10 minutes, or until lightly browned to dry it out.
Butter a 9 x 13 baking dish and set it aside.
Melt the butter in a medium skillet over medium-high heat. Add the onion, bell pepper, and celery and cook until the veggies begin to soften, about 3 to 5 minutes. Add the garlic and cook for another minute.
Place the toasted bread, cooked vegetables, and shredded chicken in the baking dish and season with poultry seasoning, salt, black pepper, onion powder, garlic powder, smoked paprika, ground sage, dried thyme, and cayenne pepper. Gently toss the ingredients together with a wooden spoon.
Add four cups of chicken broth to the pan and gently stir the dressing to moisten all of the bread. Add more broth until the dressing is a bit soupy but not completely runny. You should end up using 5 to 6 cups of broth.
Taste the cornbread dressing and add more seasoning if needed until you are pleased with the flavor. Mix in the beaten eggs. Lower the oven temperature to 375°F, transfer the dressing to the oven, and bake it uncovered for 50 to 60 minutes, or until golden brown on top and set in the center. Allow the dressing to cool for about 10 minutes and enjoy!