In a large mixing bowl, cream together the softened unsalted butter and 1 cup of granulated sugar with an electric mixer until light and fluffy (about 2-3 minutes).

Beat in the large egg until just combined.

Stir in the lemon zest, fresh lemon juice, and vanilla extract until well incorporated.

In a separate medium bowl, whisk together the all-purpose flour, baking powder, and salt.

Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix.

Cover the dough with plastic wrap and refrigerate for at least 30 minutes, or up to 2 hours. This chilling step is crucial for preventing the cookies from spreading too much and helps the coating stick.

Preheat your oven to 375°F (190°C). Line two baking sheets with parchment paper.

Place 1/4 cup of granulated sugar and 1/2 cup of powdered sugar into two separate shallow bowls for rolling.

Scoop the chilled dough by rounded teaspoons (about 1.5 tablespoons per cookie). Roll each portion into a smooth ball.

First, roll each dough ball in the granulated sugar, ensuring it's evenly coated.

Next, heavily roll each sugar-coated ball in the powdered sugar until completely covered. This double coating is essential for the crinkle effect.

Place the coated dough balls about 2 inches apart on the prepared baking sheets.

Bake for 9-11 minutes, or until the edges are set and lightly golden, but the centers still look soft. Do not overbake, as they will continue to set as they cool.

Let the cookies cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.