Sandra Fairbank's Tiny Poppy Seed Cookies

Combine the butter and sugar in the bowl of a stand mixer or hand-held mixer; beat for several minutes, stopping to scrape down the sides of the bowl as necessary, until smooth and creamy.
Add the egg, then the vanilla extract, mixing well after each addition.
Reduce speed to low and add the flour, baking powder and salt; beat until well incorporated.
Scrape down the sides of the bowl, then add the poppy seeds and lemon zest; beat until well distributed.
Divide the dough into 3 balls and place each ball inside the center of a large resealable plastic food storage bag.
Place each bag on the counter and, using a rolling pin, roll the dough from the center toward the edges until it is an even 1/4 inch thick.
Seal and refrigerate for at least 1 hour and up to 2 days.
(Alternatively, roll the dough into a compact log that is 1 inch in diameter, then wrap tightly in plastic wrap and refrigerate as directed.
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When ready to bake, position an oven rack in the middle of the oven; preheat to 400 degrees.
Line a baking sheet with parchment paper.
Remove 1 bag of dough at a time from the refrigerator.
Use a 1-inch round cookie cutter to punch out cookies (or slice 1/4-inch-thick rounds from the dough log) and place 1 inch apart on the baking sheet; gather scraps and reroll the dough as necessary.
Bake for 7 to 10 minutes or until the cookies are light golden brown.
Cool on the sheet for 5 minutes, then transfer to a wire rack to cool completely.
Repeat with the remaining dough.