Preheat oven to 350, with racks in upper and lower thirds. In a medium bowl, combine flour, salt, and baking soda. In a small bowl, mix together sugar, egg yolks, poppy seeds, oil, lemon zest, and vanilla. Stir egg mixture into flour mixture until combined (dough will be dry).
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Drop dough by teaspoonfuls, 2 inches apart, onto two parchment-lined baking sheets. Bake cookies until golden brown, 10 to 14 minutes, rotating sheets halfway through. Transfer cookies while hot to wire racks and let cool completely. Store in an airtight container up to 5 days.
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