Prepare the Chicken: Season chicken thighs with salt and pepper. Add olive oil to a deep skillet or heavy pan and cook chicken on both sides until browned, about 8-10 minutes.
Simmer the Chicken: Add water, celery, and garlic cloves to the skillet and bring to a boil. Lower to simmer, cover, and cook for 20 minutes.
Shred the Chicken: Remove chicken to a plate to cool slightly. Remove skin and bones and shred or roughly chop chicken. Set the broth aside.
Preheat Oven: Preheat oven to 350°F (175°C).
Combine Dry Ingredients: Crumble baked cornbread into a large bowl. Add seasoned stuffing crumbs.
Sauté the Aromatics: Add butter to a skillet and melt over medium heat. Add onions and celery, cook until softened. Stir in heavy cream and mix well.
Combine Wet and Dry: Pour onion mixture over cornbread mixture and add shredded chicken.
Add Broth and Eggs: Mix 2 cups of reserved broth with 2 beaten eggs, pour over dry ingredients and stir until combined.
Moisten to Perfection: Add more broth ½ cup at a time until well moistened but not runny.
Season Generously: Add garlic, sage, rosemary, salt, and pepper and mix until thoroughly combined.
Bake to Golden Brown: Pour mixture into a well-greased 9 x 13 inch baking dish, spreading evenly. Cover with foil and bake for 1 hour. Remove foil and bake another 30 minutes or until the top and edges are browned.
Let Rest and Serve: Let rest for a few minutes before serving. Enjoy!