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Preheat oven to 350 °F (check that you have an oven rack in the middle position) and line two cookie sheets with non-stick parchment paper or silicon baking sheets.
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Combine flour, 1 1/2 teaspoons baking powder, and salt in a medium sized bowl.
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Wash your lemons well and dry them with a paper towel, then zest them directly over the bowl of flour (reserve the lemons for other uses).
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Use a sharp pointy knife to split your vanilla bean lengthwise and scrape the seeds and add to the flour mixture (reserve the pod shell for other uses).
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Whisk the flour mixture well and set aside.
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Beat the butter and sugar together until they are combined and look fluffy (2-3 minutes using a stand mixer, 5 minute with a hand mixer), scraping down the sides of the bowl as needed.
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Combine the oil, water, and 2 teaspoons of baking powder in a small bowl and add to the butter and sugar mixture, add the lemon extract, and mix on low speed until combined.*
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Add flour mixture and mix on low speed until combined, scrape down sides of the bowl as needed, stop when the flour is mixed it but do not overmix.
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Gather the dough into a ball and cover with plastic wrap and refrigerate the dough for 15-30 minutes.
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Place powdered sugar in a bowl (I used the flour mixture bowl).
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Use a tablespoon sized measuring spoon to measure the dough and a regular teaspoon to scrape the dough out into the bowl of powdered sugar.
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Use your fingers to roll the dough in the powdered sugar and shape it into a ball.
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Place the powdered sugar covered dough on your prepared cookie sheet about 2 inches apart from each other, repeat measuring and rolling the dough
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Bake for 12-13 minutes until the cookies are puffy, slightly cracked, and golden brown at the bottom.
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Allow the cookies to cool on the tray for a few minutes then transfer to a wire rack to cool completely.