Add sugar and lemon zest to a small bowl. Use your fingers to rub zests into sugar.

Beat butter in a large bowl until creamy. Add lemon sugar. Beat until light and fluffy.

Add egg and vanilla. Beat until combined.

Whisk together flour, salt, and baking soda. Add to butter mixture, alternately with sour cream, and beat until just combined.

Divide dough in half. Form each half into a 7-inch log. Wrap logs in parchment paper or plastic wrap. Chill logs thoroughly, at least 4 hours or overnight.

Heat oven to 375°F. Line baking sheets with parchment or non-stick liner.

Unwrap logs and cut into 1/4-inch slices. Place slices 1 inch apart on baking sheets.

Bake 8 to 10 minutes, or until edges are lightly browned.

Cool cookies 1 minute on baking sheet. Transfer cookies to a wire rack and cool completely.