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Preheat oven to 425°F and set aside a parchment lined baking sheet.
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Combine water, butter, sugar, and salt together in a medium saucepan over medium heat. Bring to a boil.
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Once the butter has melted, quickly add the flour and stir until the flour has absorbed all of the liquid and the dough has formed a ball. Remove from heat and transfer the dough to a large bowl. Allow it to cool for 3 minutes.
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Using a wooden spoon or stand mixer running on low speed, mix in eggs and vanilla, one at a time. Make sure to mix well after each addition. Initially, the batter will look curdled, but rest assured that by the addition of the final egg, the batter will be smooth and of perfect consistency.
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Transfer batter to a piping bag and pipe 2-inch mounds (about 1 to 2 tablespoons worth), placed a few inches apart. Alternately, you can use spoons to place dollops of batter on the pan.
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Bake for 10 minutes. Turn temperature down to 350°F and bake for an additional 25 minutes.
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Remove from the oven and transfer to a wire rack to cool completely.