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Preheat oven to 400 degrees. Line 2 baking sheets with parchment paper.
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In a heavy bottomed saucepan, combine butter and water. Bring to a boil on medium heat.
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In a separate bowl, combine flour, sugar and salt. Whisk together.
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When butter water is boiling, remove from heat and add flour mixture using a wooden spoon.
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Continue to combine until a smooth ball forms that is no longer sticking to the sides.
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Return pan to medium heat and continue to mix constantly for 2 minutes.
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Remove from heat and place dough into a mixer fitted with a paddle attachment or your hand mixer.
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Mix for 2 minutes on low to cool down.
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In a small bowl combine 4 eggs and whisk together.
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Slowly add ⅔ of egg mixture to your dough and mix on low.
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Increase you mixer to medium high and continue to mix until dough becomes thick again.
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Add the rest of the egg and mix again for about 2 minutes.
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Scoop out tablespoon rounds 2 inches apart on your baking sheets.
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Bake for 15 minutes at 400 degrees then reduce temperature to 350 degrees and bake for another 15-30 minutes, depending on your oven.
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Keep an eye on them, if they begin to brown too quickly turn your oven off.
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Once done, remove from oven and make a small whole using a toothpick into the puffs.
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Return baking sheets to a hot (but turned off oven) and allow to cool with the oven door cracked open slightly (I folded a oven glove to keep door open slightly).
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Allow puffs to cool completely in oven (about an hour).