When you're making this dressing, it's essential to buy fresh oysters and shuck them on the same day. Be sure to chop the oysters into large pieces.Plus: Ultimate Holiday Guide
Preheat the oven to 450°. Line a 12-by-16-inch rimmed baking sheet with parchment paper and lightly grease the paper. In a large bowl, whisk the flour with the cornmeal, sugar and salt. In another bowl, whisk the milk with the eggs, melted butter and shallots. Stir the milk mixture into the dry ingredients until blended. Spread the batter on the prepared baking sheet and bake for 12 minutes, or until the corn bread is firm in the center. Transfer to a rack and let cool in the pan, about 30 minutes. Reduce the oven temperature to 350°.
Butter a deep 9-by-13-inch casserole. In a large skillet, melt the butter. Add the celery, garlic, onion and thyme and cook over moderate heat, stirring frequently, until the celery is softened, 8 minutes. Discard the thyme sprig. In a large bowl, break the corn bread into 1-inch pieces. Stir in the celery mixture, the oysters and their liquor, the broth, lemon zest, lemon juice and parsley. Season with salt and pepper; mix in the eggs. Spread the dressing in the casserole. Cover with foil and bake for 40 minutes; uncover and bake for 25 minutes longer, or until the top is lightly browned.
Once assembled, the dressing can be refrigerated for 4 hours. Bring to room temperature before baking. The baked corn bread can be wrapped and frozen for up to 2 weeks. Thaw before using.