Preheat your grill to 350F.
Place the cubed bread on a sheet pan and bake 30-40 minutes until dried out, but not golden brown.
Remove from grill and allow to cool. This can be done in advance.
On the stovetop, heat a cast iron skillet and add 3 T butter, onion and celery. Sauté for several minutes until translucent.
Add the herbs, and season with salt and pepper. Stir well and cook for an additional minute or two to combine the flavors.
In a small bowl, beat the two eggs with 1 cup of chicken broth.
In a large mixing bowl, add the dried bread cubes and top with the celery and onion mixture. Mix well.
Add the broth and egg mixture and stir to combine. Add additional broth until bread is spongy but not soggy.
Place the stuffing mixture in the cast iron skillet and grill at 350F, 45-50 minutes.
In another skillet, add the remaining 3 T butter, the mushrooms and the fennel. Place skillet with the mushrooms and fennel on the grill and cook until caramelized, stirring occasionally.
Top the stuffing with the fennel and mushrooms and garnish with reserved fennel fronds.
Enjoy warm.