How to Make It
Combine flour, sugar, lemon zest, baking powder, baking soda, and salt in the bowl of a food processor. Pulse to mix.
Scatter butter across surface. Pulse until butter is completely incorporated into dry ingredients. Add buttermilk and pulse a few times until the dough clumps together. Gather dough, barely kneading until you can shape the dough into a ball. Wrap in plastic wrap and refrigerate 1 hour.
Preheat oven to 350°F. Line a rimmed baking sheet with parchment paper; set aside. On a well floured surface, use a floured rolling pin to roll dough into a 1/4-inch thick circle. Use a 3-inch round cutter to punch out circles from the dough; transfer circles to prepared baking sheet. Reroll scraps and cut out additional circles.
Bake until tea cakes have puffed slightly and barely take on color, 12-14 minutes. Allow to cool slightly before removing from baking sheet.