In a medium bowl, whisk together the flour, baking powder, and salt until evenly combined. Set aside.

In a large bowl, beat the softened butter and 1 cup granulated sugar with an electric mixer on medium speed until light and fluffy, about 2-3 minutes.

Add the eggs one at a time, beating well after each addition. Mix in the lemon juice, lemon zest, and vanilla extract until fully incorporated.

Add the dry ingredients to the wet ingredients and mix on low speed just until a soft dough forms. Do not overmix.

Cover the bowl with plastic wrap and refrigerate the dough for at least 30 minutes, or up to 3 days.

Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone mats.

Place the 1/4 cup granulated sugar in a small bowl and the powdered sugar in a separate small bowl. Scoop about 1.5 tablespoons of dough and roll into a ball.

Roll each ball first in the granulated sugar to coat completely, then roll generously in the powdered sugar until fully covered. Place the coated balls on the prepared baking sheets, spacing them about 2 inches apart.

Bake for 10-12 minutes, until the cookies have spread slightly and developed cracks on top, but still look soft and underdone in the centers. The edges should be barely set.

Let the cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely. The powdered sugar coating will stay bright white as they cool.