In a food processor, combine the room temperature unsalted butter and icing sugar, pulsing until light and fluffy. Gradually add the all-purpose flour, fine sea salt, Earl Grey tea leaves, and your choice of Earl Grey or vanilla extract. Pulse until a cohesive dough forms, about 1-2 minutes.

Divide the dough into two equal portions, rolling each into logs about 1.5 to 2 inches in diameter. Wrap each log tightly in plastic wrap and refrigerate for at least 1 hour.

Preheat your oven to 350°F (175°C). Remove chilled dough logs, slice them into ¼ to ½ inch thick pieces, and arrange on a parchment-lined baking sheet.

Bake for approximately 10 minutes, keeping an eye on them. Let cookies cool on the sheet before transferring to a wire rack.