Melt butter in a pan on medium heat. Add water. When it begins to lightly boil, lower the heat and add flour and salt. Stir mixture quickly with a wooden spoon until it becomes a ball in the center of the pan. Add the vanilla extract. Use a mixer to mix in one egg at a time.
Dip a tablespoon in water. Scoop one heaping spoon of batter onto a baking sheet. Space out one to two inches in-between.
Bake for 45 minutes. Once puffs have cooled, cut a slit half way across the top. Squeeze sides and scoop in pudding mixture.