Whisk pumpkin puree, 1/4 cup sugar, egg whites, egg, cinnamon, ginger, and cloves together in a bowl until smooth.
Heat remaining 1/2 cup sugar in a saucepan over medium heat, stirring constantly, until dissolved, 3 to 5 minutes. Spoon dissolved sugar into the bottom of 6 custard cups.
Pour evaporated milk into a microwave-safe bowl. Microwave in 30-second intervals until warmed through, 1 1/2 to 2 minutes. Stir into the pumpkin mixture. Pour pumpkin mixture over the sugar in the custard cups.
Place custard cups in a deep baking pan. Pour in water around the custard cups to a depth of 1 inch.
Bake in the preheated oven until custard is set in the center, 30 to 35 minutes. Remove from water and chill until cold, about 2 hours.