Combine the melted butter and brown sugar in a baking dish. Arrange the bread slices in the dish. Whisk together the eggs, milk, vanilla, cinnamon, ginger, and salt in a bowl. Pour over the bread, letting it soak in. Top with the pecans. Cover with plastic wrap and refrigerate for at least 3 hours and up to 12 hours.
Preheat the oven to 350°F. Let the chilled casserole stand at room temperature for 20 minutes.
Bake until browned and set, 30 to 45 minutes. Remove to a rack to cool slightly. Sift over confectioners’ sugar. Serve hot or warm with sorghum, cane, or maple syrup.