Preheat and prep: Heat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
Mix dry ingredients: In a bowl, whisk 2 1/4 cups all-purpose flour, 1/2 teaspoon baking soda, and 1/2 teaspoon fine sea salt.
Set aside.
Rub zest into sugar: In a large bowl, combine 1 cup granulated sugar with the zest of 1–2 lemons. Use your fingers to rub the zest into the sugar until fragrant and slightly damp. This boosts the lemon flavor.
Cream butter and sugar: Add 3/4 cup room-temperature unsalted butter to the lemon sugar.
Beat until light and fluffy, about 2–3 minutes.
Add wet ingredients: Beat in 1 large egg, 1 teaspoon vanilla extract, 1 tablespoon fresh lemon juice, and 1/2 cup unfed sourdough starter until smooth. The mixture may look slightly curdled at first—keep mixing.
Combine: Add the dry ingredients and mix on low just until no dry streaks remain. Do not overmix.
The dough should be soft and scoopable.
Roll in sugar: Pour 1/3 cup granulated sugar into a shallow bowl. Scoop dough into 1 1/2 tablespoon portions (about cookie-scoop size), roll into balls, then coat in sugar.
Arrange and bake: Place on baking sheets, spaced 2 inches apart. Bake 10–12 minutes, until edges are set and centers still look soft and slightly underdone.
Optional crinkle finish: Halfway through baking, gently lift the sheet a few inches and let it drop.
Repeat once more at the end. This helps create crackly tops.
Cool: Let cookies rest on the baking sheet for 5 minutes, then move to a rack. They’ll finish setting as they cool.