Slice the french bread and cornbread into bite-size cubes and let them sit out for 1-2 days in a single layer on a baking sheet to dry out.
Preheat oven to 350 degrees F.
Melt 4 tablespoons of the butter in a large skillet over medium heat. Add the onion and celery and cook for 4-5 minutes until softened. Add the garlic and cook for an additional 30 seconds.
Add the chicken broth, basil, thyme, sage, rosemary, and parsley to the vegetables. Bring to a simmer.
In a separate bowl, melt the remaining butter, then add the eggs, salt, and pepper, and beat until combined.
Combine the dried bread cubes in a very large bowl and drizzle with the egg mixture.
Begin to add the warm broth mixture to the dried bread, a little at a time. Toss lightly so that everything gets evenly moistened. You may not need all the broth. Stop adding liquid if the dressing starts getting mushy.
Transfer the dressing to a large 9x13-inch baking dish, then bake uncovered for 25-30 minutes until hot all the way through and golden brown on top.