Preheat the oven to 350F (180C). Oil or butter a 9x13-inch baking dish or casserole dish and set aside.
Slice the cornbread into 1-inch cubes. Add the cubed cornbread to a large baking sheet in a single layer. Use two baking sheets if needed.
Bake for 20-30 minutes, tossing halfway through the cook time, or until the cornbread is toasted and dried. Set aside.
Add the butter to a large skillet or cast iron pan over medium heat. Let the butter melt.
Add the diced onion, celery, salt and pepper to the skillet. Cook for 4-5 minutes, until translucent.
Add the minced garlic and cook for 1 minute, stirring frequently so the garlic doesn't burn.
Add the lump Italian sausage to the pan. Stir to break up the pieces of sausage. Cook for 6-8 minutes, until the sausage is cooked through.
Add the dried cranberries, chopped pecans, fresh sage, fresh thyme, and fresh parsley. Stir until combined.
Pour the mixture, including any oil or spices left in the pan, into a large bowl.
Top with the cornbread cubes.
In a measuring cup, combine 2-3 cups (see notes) of the gluten-free chicken broth and the eggs and whisk until smooth. Pour the mixture over the stuffing mixture. Gently toss to combine, trying to keep the cornbread from crumbling.
Pour the stuffing into the prepared 9x13-inch pan.
Bake at 350F for 40-50 minutes, until the top of the stuffing is golden and crispy and the center no longer feels wet.
Serve warm.