Preheat the oven to 375 degrees F. Spray a 1 1/2 quart souffle dish with non-stick spray.
Put the dates and water in a pot over medium-low heat. Cook and stir for 10 minutes until the dates are very soft. Transfer the softened dates to a food processor and puree until smooth. Add the sugar and vanilla, puree again until well-blended. Scoop out the puree into a mixing bowl. Sift together the cocoa powder and flour and add to the date mixture. Fold using a rubber spatula; combine gently until well mixed.
In a mixing bowl, whip the egg whites until they form stiff peaks. Fold the egg whites into the date mixture.
Pour the batter into the coated souffle dish, spreading it evenly with a spatula. Bake on the middle rack for 25 minutes until the outside is just set. Cool to room temperature. Shake some confectioners' sugar on top and serve.