Heat the oven to 375°F (190°C). Butter a 2-quart baking dish with 1 tablespoon of the butter.

Melt the remaining butter in a saucepan. Add the onion and celery and cook over medium heat for 8 to 10 minutes, until fully soft.

Add the broth, milk, sage, salt, and pepper. Bring to a gentle simmer, whisk in the cornmeal, and cook for 5 to 7 minutes until thick and smooth.

Remove from the heat and cool for 10 minutes. Whisk a small amount of the warm cornmeal into the eggs, then fold the egg mixture back into the pot.

Pour into the prepared dish and bake for 35 to 45 minutes, until the edges are set, the top is pale gold, and the center still trembles gently.

Let the spoonbread dressing rest for 10 minutes, then serve warm with a large spoon.