Sift together flour, baking soda, and salt in a medium bowl and set aside.
Pulse butter, sugar, lemon zest, and basil in a food processor until light and fluffy.
Add egg and lemon juice to the processor and pulse until smooth.
Add half of the dry ingredients to the processor and pulse until just combined; then add remaining dry ingredients and pulse until a smooth dough forms.
Shape the dough into a 1-inch diameter log, roll in granulated sugar, wrap tightly in cling wrap, and chill for at least one hour.
Preheat oven to 350°F and line a baking sheet with silpat or parchment paper.
Unwrap and slice the chilled dough log into 1-inch discs; optionally coat both sides with sugar.
Place discs 2 inches apart on the prepared baking sheet and bake for 10-12 minutes until edges just start to turn golden.
Let cookies rest on the baking sheet for 2 minutes before transferring to a wire rack to cool completely.
Store cooled cookies in an airtight container in a cool, dry place for up to 5 days.