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To make the dough: In a small bowl, whisk together the flour, baking powder, and baking soda. Set aside.
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In a large bowl, whisk together the sugar and lemon zest until the zest is evenly distributed. Add the oil, butter, vanilla, and salt. Whisk until smooth, then whisk in the lemon juice. Add the egg and whisk until combined.
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Add the dry mixture and use a flexible spatula to stir until the flour is fully incorporated and there are no dry spots. The mixture will be very soft.
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Cover the bowl and chill the dough in the refrigerator for 2 to 3 hours, or up to 2 days. It will firm up considerably.
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When you are ready to bake, preheat the oven to 350°F with racks in the upper and lower thirds. Line 2 baking sheets with parchment.
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To shape the lemon crinkle cookies: To coat the cookies, place the granulated sugar in a small bowl and the confectioners’ sugar in a medium bowl.
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One at a time, scoop the dough into 1 1/2" balls (about 23g each; a level tablespoon cookie scoop works well here) and place it directly into the bowl of granulated sugar. Toss to coat, then transfer to the bowl of confectioners’ sugar and, again, toss to coat. Transfer the coated lemon crinkle cookie to the prepared baking sheet and repeat with the remaining dough. The dough will still be soft but will hold its shape when placed on the baking sheet.
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Bake the lemon crinkle cookies for 11 to 13 minutes, rotating the pans halfway through baking. They will be slightly puffed in the center, the edges will be firm, and the centers will be set.
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Remove from the oven and allow the cookies to cool completely on the baking sheet; serve warm or at room temperature.
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Storage information: Store leftover lemon crinkle cookies in an airtight container at room temperature for several days; freezing is not recommended.
