Heat the sugar in a heavy medium saucepan over medium heat, stirring constantly, until the sugar is melted, smooth, and golden brown in color. Pour the syrup into the 8-inch baking dish and pick it up immediately; swirl to coat the bottom with the caramel. You just want to ensure an even coating of the caramel before it has a chance to harden. Place the baking dish back in the larger dish of water and set aside.

Beat the whole eggs and egg whites with the pumpkin, maple syrup, spices, vanilla, and salt until smooth. Whisk in the milk until well blended. Pour the custard mixture over the caramel layer. Bake the flan for 50 to 60 minutes or longer, until a knife inserted into the center of the flan comes out clean. Remove the flan to a rack and cool to room temperature about 1 hour. Refrigerate to chill thoroughly for about 4 hours or overnight.

To unmold the pumpkin flan, place the baking dish in about 1/2 inch of warm water for about 30 seconds. Run a knife or small icing spatula around the edge of the flan to loosen the sides. Jiggle the dish gently to loosen the bottom a bit more, and then place a platter or serving plate over the top of the baking dish. Invert and jiggle gently until the flan releases to the serving plate. Let stand for a few seconds to let excess caramel adhering to the baking dish drip onto the flan.

Cut the flan into squares or triangles to serve. Spoon a little of the caramel sauce over each serving.