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Preheat oven to 375 degrees F and line two large baking sheets with parchment paper.
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In saucepan, bring to boil water, butter, sugar and salt, stirring to combine. When butter is dissolved, reduce heat to low, add flour and stir to bring together to form ball. Cook 2-3 minutes, stirring vigorously until a film forms on bottom of pan. Turn off heat and allow dough to sit for 5 minutes to cool slightly.
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Add eggs one at a time, stirring vigorously until completely combined and dough becomes a paste-like mixture. (Note: Stir by hand, or transfer dough to stand mixer with paddle attachment.)
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Add pastry dough to piping bag fitted with ½-inch-wide plain tip. Onto prepared baking sheets, pipe mounds that are 1-inch high and ¾-inch in diameter, placing them about 1 inch apart. Using wet finger, tap down any points on pastry to make surface smooth.
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Place baking sheets in oven and immediately turn temperature up to 400 degrees F. Bake 15 minutes. Turn temperature down to 350 degrees F and bake for an additional 10–15 minutes, or until pastry puffs are golden brown and sound hollow when tapped. Turn off oven and allow pastries to cool inside with door slightly open for 20 minutes. (Note: Slightly prop open door with handle of wooden spoon, if needed.)
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Remove from oven, poke hole in bottom of each pastry puff and allow to cool completely on wire rack.