1. Preheat oven to 300 degrees with rack in center. In a large bowl, whisk together eggs, half-and-half, maple syrup, and salt. Stir in cornbread; let sit, tossing occasionally, until bread has absorbed liquid, about 5 minutes (bread will break down into small pieces).

2. Pour mixture into an 8-inch square (2-quart) baking dish; flatten and smooth top with a spoon or flexible spatula. Bake until a toothpick inserted in center of pudding comes out clean, 1 hour to 1 hour 15 minutes. Let cool 10 minutes.

3. Serve with more maple syrup (and ice cream or heavy cream, if desired) on top.