Preheat the oven to 350?F. Grease a 9 x 13-inch casserole with 1/2 tablespoon butter and set aside.
Melt the remaining 3 tablespoons butter in a large skillet over medium heat. Add the sliced onions and cook until tender and beginning to caramelize, about 20 minutes, stirring frequently, and adding a bit of water if the onions begin to brown before they have softened. Season with a pinch of salt, remove from the heat, and set aside.
Add the eggs, cornmeal, heavy cream, and milk to a large bowl and whisk to combine. Stir in the remaining ingredients, including the finely chopped onions, and pour the mixture into the prepared casserole. Top with caramelized sliced onions and bake on the middle rack for 45 minutes, or until the pudding is golden brown on top. Serve warm.
Makes 10 servings