Preheat oven to 350 degrees. Place a heavy 2-quart baking dish or a heavy 13×9 pan in the oven.
Heat the olive oil and butter over medium heat in a large, heavy, nonstick skillet, and add the onion.
Cook, stirring often, until it begins to soften, about 3 minutes, and add 1/2 teaspoon salt and the celery.
Cook together for another few minutes, until the onion is tender.
Add the garlic, and stir together for 30 seconds to a minute, until fragrant.
Transfer to a large bowl and add Cornbread broken to pieces.
Combine well. Taste and adjust salt.
Moisten as desired with milk.
Bake for 30 minutes or until the internal temperature is 160 degrees