Step 1: In a medium bowl, combine the finely ground Earl Grey tea leaves with the softened unsalted butter. Allow the tea to infuse the butter for at least 15-20 minutes at room temperature, or up to an hour for a stronger flavor.
Step 2: In a large mixing bowl, cream together the tea-infused butter and granulated sugar with an electric mixer until light and fluffy.
Step 3: Beat in the egg yolk and vanilla extract until well combined. Scrape down the sides of the bowl as needed.
Step 4: In a separate bowl, whisk together the all-purpose flour and salt. Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined and a soft dough forms. Be careful not to overmix.
Step 5: Divide the dough in half, flatten each half into a disc, wrap tightly in plastic wrap, and refrigerate for at least 1 hour, or until firm enough to roll.
Step 6: Preheat your oven to 350°F (175°C) and line baking sheets with parchment paper.
Step 7: On a lightly floured surface, roll out one disc of chilled dough to about ¼-inch thickness. Use a 2-inch round cookie cutter (or a cutter of your choice) to cut out shapes. Reroll scraps as needed.
Step 8: Place the cut-out cookies about 1 inch apart on the prepared baking sheets.
Step 9: Bake for 10-12 minutes, or until the edges are lightly golden. The centers may still look soft but will firm up as they cool.
Step 10: Remove from the oven and let the cookies cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.