Preheat your oven to 350°F (175°C). Line two rimmed baking sheets with silicone baking mats or parchment paper, and add the powdered sugar to a small bowl for rolling.
Wash and dry the lemons, then zest them using a Microplane, collecting 1 tablespoon of zest while avoiding the bitter white pith. Cut and juice the lemons to get 2 tablespoons of fresh juice, straining out any seeds.
In a medium bowl, whisk together the flour, baking powder, and salt until evenly combined, then set aside.
In a large bowl using a stand mixer or hand mixer, beat the softened butter and granulated sugar on medium-high speed for 3 to 4 minutes, until pale, light, and fluffy, scraping the bowl as needed.
Add the eggs one at a time, mixing well after each addition. Then mix in the lemon juice, lemon zest, vanilla extract, lemon extract (if using), and food coloring (if using) until fully combined.
With the mixer on low speed, add the flour mixture in two additions, mixing just until no dry streaks remain — do not over-mix.
Use a 1.5-tablespoon cookie scoop to portion the dough into balls, roll each one smooth between your palms, then generously coat each ball in the powdered sugar. Place them 2 inches apart on the prepared baking sheets.
Bake at 350°F (175°C) for 11 to 13 minutes, until the edges are set and the tops have crinkled; the centers may look slightly underdone, which is correct.
Let the cookies rest on the baking sheet for 5 minutes, then transfer to a wire rack to cool for at least 10 more minutes. Dust with extra powdered sugar before serving if desired.