Place the all-purpose flour, baking powder, baking soda, salt, and poppy seeds in a medium-sized bowl and whisk together for about 30 seconds to combine the ingredients.
Place the granulated sugar in the bowl of a stand mixer. Zest the lemons directly into the bowl on top of the sugar. Use your fingers to rub the lemon zest into the sugar for about 1 minutes until the sugar turns a light yellow and starts to clump together like wet sand. Juice the lemons until you have about 2 tablespoons.
Add the brown sugar and the butter to the bowl of the mixer. With the paddle attachment, mix on low speed for 30 seconds and then increase to medium speed and beat for 3 minutes until the dough is cream and lighter in color. Scrape down the bottom and sides of the bowl. Scrape the dough off the paddle attachment.
Add the egg and mix on medium speed for about 30 seconds until it is well incorporated and the dough looks creamy. Add the lemon juice and vanilla extract and mix on medium speed until both are incorporated. Scrape the bottom and the sides of the bowl.
Add the dry ingredients to the dough and mix on low speed until the flour is fully incorporated. Stop the mixer and scrape down the sides and bottom of the bowl and the paddle attachment to ensure the dough is fully mixed and to mix in any flour that is on the sides of the bowl.
Scrape the dough into a smaller bowl and refrigerate the dough for at least 1 hour and up to 3 days.
Preheat the oven to 350°F. Line two half baking sheets with parchment paper. If you only have one baking sheet, always wait until the baking sheet has completely cooled before placing raw cookie dough on the baking sheet.
Scoop 2 tablespoons (30 grams) of the cookie dough and place them in a 2-1-2-1 pattern on the cookie sheet about 3-inches apart. An easy way to scoop the cookies is to use a #40 cookie scoop, which holds about 2 tablespoons.
Bake the cookies for 10-11 minutes until the edges are light golden brown. Remove the cookies from the oven and let cool on the baking sheet for 3 minutes before moving the cookies to a wire rack to finish cooling.
If you want perfectly round cookies as soon as the cookies come out of the oven place a round cookie cutter around one of the cookies on the baking sheet. (It should be bigger than the cookie, and therefore not cut off any of the edges.) Then, use the cookie cutter to mold the edges of the cookie from uneven to perfectly round, using a swirling motion.