WET INGREDIENTS: Add 1 cup butter to the base of a stand mixer (or use a large bowl and a hand mixer). Add in 1-1/2 cups white sugar and 3 tbsp lemon zest. Beat until creamy, about 2-3 minutes. Scrape sides and add in 2 eggs, 1 tsp vanilla, and 2 tsp. lemon extract. Beat until incorporated.
DRY INGREDIENTS: Scrape sides and add 2 tsp baking powder, 2 tbsp. poppyseeds, and 1 tsp salt. Mix to combine. Finally, add in the flour and beat just until combined and no streaks of flour remain.
CHILL: Cover dough tightly and chill in fridge for 20 minutes. Line a large plate with parchment paper.
FORM COOKIE DOUGH BALLS: Portion out dough, measuring each ball to be exactly 1/4 cup (60 grams) of dough (I don't recommend bigger or smaller cookies -- they work best in this size -- Note 5) Repeat with remaining dough to get about 16-18 cookie dough balls. Once dough balls are rolled, roll each dough ball in 1/2 cup white (or coarse) sugar and then set them on the parchment-lined plate.
CHILL AGAIN: Return to the fridge for 30 minutes or freeze for 20. Meanwhile, preheat the oven to 325 degrees F (162 degrees C). Line a large sheet pan with parchment or a Silpat liner.
BAKE AND COOL: Add cookies to the prepared pan, only 6 at a time (they need a lot of space to spread!). Keep the rest of the dough balls in fridge/freezer while baking. Bake for 12-16 minutes or until cookies have puffed up and aren't gooey or wet looking on top. Bottoms/edges should be ever so slightly browning. Be careful to not overbake as you'll lose out on flavor and texture! Remove from oven, let stand on sheet pan for 5 mins before removing to a wire cooling rack to fully cool. Do not glaze until completely cooled. Repeat to bake all the cookies or save some for later (See Instruction #8)
GLAZE: Meanwhile, combine all the glaze ingredients in a medium bowl. Whisk until smooth. Transfer to a small zip-top bag and seal without air. Cut the tip off the bag and drizzle glaze evenly over all of the cookies. If desired, add a touch of lemon zest to the top. Enjoy at room temperature or chilled.
STORAGE: Instead of freezing baked cookies, freeze the dough! Drop the cookie dough balls on a large sheet pan and freeze until solid. Once solid, transfer the frozen cookie dough balls to an airtight container or bag and freeze for up to 3 months. To bake: You can bake these lemon cookies straight from the freezer. There is no need to thaw, but you may need to add a few extra minutes to the baking time. Bake until the edges are lightly browned, and the center is still soft.The glaze doesn't freeze and thaw well, so I recommend making that fresh.