Preheat the oven to 375°F
Crumble baked cornbread into a large bowl
Add cubed day-old bread or breadcrumbs
Mix in chopped onion and celery
Add melted butter
Stir in beaten eggs
Pour in chicken or turkey broth
Add salt, black pepper, sage, and thyme
Mix until evenly moistened
Fold in cooked sausage or chopped hard-boiled eggs if desired
Transfer the mixture to a greased baking dish
Bake for 30 to 45 minutes until set and golden on top
Let cool slightly before serving