Preheat a grill to medium high. Stack two 12-inch-long pieces of heavy-duty foil. Toss the blackberries, 2 tablespoons sugar and the butter on the foil. Bring the short ends of the foil together and fold to seal, then fold in the sides and seal. Grill until the fruit is bubbling and the juices are syrupy, 12 to 15 minutes. Transfer the berries to a bowl.
Meanwhile, whisk the eggs, half-and-half, the remaining 1/4 cup granulated sugar, the vanilla, cinnamon, nutmeg and a pinch of salt in a bowl until well combined. Put the challah in a 9-by-13-inch baking dish. Pour the egg mixture on top and let soak, turning to coat, 1 to 2 minutes. Thread onto 6 skewers (if using wooden skewers, soak them in water for about 20 minutes first). Grill, turning, until well marked, 6 to 8 minutes. Transfer to a platter and dust with confectioners' sugar. Drizzle with maple syrup and serve with the blackberry sauce.