In a large mixing bowl, combine the granulated sugar and lemon zest. Use your fingertips to rub the zest into the sugar for about 1 minute until fragrant. This helps release the lemon oils and enhances flavor.

Add the eggs, vegetable oil, fresh lemon juice, and vanilla extract to the lemon sugar mixture. Beat with an electric mixer on medium speed until well combined and light in color, about 2-3 minutes. Scrape down the sides of the bowl as needed.

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; overmixing can lead to tough cookies. The dough will be soft and sticky.

Cover the bowl with plastic wrap and refrigerate the dough for at least 1 hour, or up to 24 hours. Chilling is crucial for the dough to firm up and for achieving those signature crinkles.

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

Place the powdered sugar for rolling in a small, shallow bowl.

Scoop rounded tablespoons of the chilled dough and roll them into 1-inch balls. Generously roll each dough ball in the powdered sugar, ensuring it's completely coated. The thicker the powdered sugar coating, the more pronounced the crinkles will be.

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

Bake for 10-12 minutes, or until the edges are lightly set and the cookies are puffed and crinkled. The centers may still look slightly soft. Do not overbake, as they will continue to set as they cool.

Remove the baking sheets from the oven and let the cookies cool on the sheets for 5 minutes before transferring them to a wire rack to cool completely.