In a saucepan combine the water and butter, and bring to a boil. Drop all the flour into the pot and stir vigorously until the dough forms a ball, and breaks free from the sides of the pot.
Remove from the heat. Beat in eggs, ONE AT A TIME, stirring well before next egg is added.
Mix until a sticky dough is formed. Spoon onto a large cookie sheet, tucking in any peaks.
Bake at 450°F for 20 minutes, then reduce heat to 350°F and bake for another 20 minutes. During the last 5 minutes stab each puff with a sharp knife to release the steam. Remove from the oven, and let puffs cool.
Combine the whipping cream, icing sugar and vanilla in a large bowl. Beat until stiff peaks form.
Slice the puffs open like a bun, and fill with cream. Dust tops with icing sugar.