Step 1

Whisk flour, lemon zest, baking powder, salt, and lavender (if using) in a medium bowl. Whisk eggs, lemon juice, and vanilla extract in a small bowl.

Step 2

Beat butter and granulated sugar in the bowl of a stand mixer fitted with the paddle attachment on medium speed until pale and creamy, about 2 minutes. Add egg mixture and beat 1 minute to combine. Reduce speed to low and add dry ingredients in 3 batches, mixing just until combined after each batch before adding more. Dough will be very soft at this point. Cover bowl and chill dough at least 1 hour and up to 2 days. (If chilling longer than 1 hour, transfer to an airtight container; this will keep the dough from drying out.)

Step 3

Place racks in middle and lower thirds of oven and preheat to 350°. Place powdered sugar in a small bowl. Using a #60 or #70 cookie scoop (or 1 Tbsp.), portion out dough and roll into balls. Working quickly so dough doesn’t have a chance to warm up, drop each dough ball into powdered sugar and roll to coat evenly. Divide cookies between 2 parchment-lined baking sheets, spacing 2" apart.

Step 4

Bake cookies, rotating baking sheets top to bottom and front to back halfway through, until puffed and cracked and edges are set, but centers are still soft (cookies will look underbaked between the cracks), 10–13 minutes.

Step 5

Let cookies cool on baking sheets before serving.Do ahead: Cookies can be baked 3 days ahead. Store airtight at room temperature.