Heat the oven to 350°F. Using 1 tablespoon of the butter, grease an ovenproof gratin or casserole dish.

Drain the oysters in a fine-mesh sieve set over a bowl, reserving the oyster liquor. Measure the liquid and add stock to make at least 2½ cups liquid.

Coarsely chop the oysters into ½-inch pieces. Set aside.

Combine the cornbread and cubed bread in a large bowl.

Melt 4 tablespoons of the butter in a large skillet over medium heat. Add the celery and onion and cook until soft, 5 to 7 minutes. Transfer the cooked vegetables to the bowl with the bread mixture. Pour the stock mixture over the bread and add the chopped oysters, eggs, sage, and thyme. The mixture should be fairly soupy. Season with salt and pepper. (If you want to taste and adjust for seasoning, simply zap a teaspoon or so of the mixture in a bowl in the micro­wave to cook the eggs and season as needed.)

Transfer the mixture to the prepared baking dish. Cut the remaining 1 tablespoon butter into bits and dot them over the dressing. Bake until heated through, puffed, and golden brown, about 45 minutes. Let cool slightly before serving.