Arrange the cornbread and French bread pieces in an even layer on a large sheet pan. Bake at 350°F for 20-30 minutes until dried out.
Melt butter over low-medium heat. Add the onion, celery, sage, thyme, salt, and pepper. Cook until the onion and celery start to soften.
Carefully pour the chicken broth into the pan, and stir to combine.
Bring to a simmer and cook for 5-7 minutes. Remove from heat.
Transfer the dried bread pieces into a large bowl. Pour the warm broth mixture over the bread pieces a little at a time.
Use a large, wooden spoon to toss the ingredients and ensure the bread is evenly moistened. Add additional broth a little as a time as needed.
Transfer the dressing into the prepared baking dish. Bake uncovered at 350°F for 25-35 minutes or until the top is golden brown.
The dressing is done when a knife inserted in the center comes out clean.
Serve hot with your favorite entree.
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