Put the butter and confectioners' sugar in a food processor, and process until smooth. Pulse in the egg, vanilla, and lemon zest until combined. Add the flour mixture and process to make a soft buttery dough. Divide the dough in half onto 2 (12-inch long) sheets of plastic wrap. Using the plastic, shape into rough logs. Refrigerate the dough logs for 30 minutes until just firm enough to shape into uniform logs, 8-inches long by 2-inches in diameter. Refrigerate until firm, at least 2 hours or overnight.
Preheat oven to 325 degrees F.
Scatter either the sanding sugars or toasted nuts on a work surface and roll the logs until completely coated. Cut into 1/4-inch thick cookies and space about 1 inch apart on parchment-lined baking sheets. Bake until golden around the edges, 20 to 25 minutes. Cool cookies on the pan on wire racks. Store in an airtight container at room temperature for up to 2 weeks.