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Preheat the oven to 350°F. Lightly grease (or line with parchment) two baking sheets. Fit a piping bag with a 1/2" round tip.
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Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess.
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In a medium bowl, whisk together the flour, baking soda, and baking powder. Set aside.
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In a large bowl, whisk the melted butter with the sugar and salt.
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Add the egg whites, water, vanilla, and vinegar and whisk until smooth.
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Fold the dry ingredients into the wet ingredients, stirring until smooth.
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Immediately transfer the batter to the prepared piping bag. Pipe 1" mounds of batter onto the prepared baking sheets, leaving about 1" between them (the cookie do not spread dramatically). You should be able to fit all of the cookies on the two baking sheets.
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Once all the batter has been piped, dip your fingers in some water and lightly press down on the top of each cookie to create a smooth surface.
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Bake the cookies for 15 to 20 minutes, until the edges are browned. Rotate the pans halfway through the bake time to ensure even browning. For cookies that remain somewhat soft in the center, aim for light browning around the edges. If you’d like a crispier cookie, bake until the edges are golden brown.
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Remove the cookies from the oven and cool completely on the pan.
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Store cookies in an airtight container for a week; freeze for longer storage.