In a large bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy. This takes about 3 minutes.
Beat in the egg and 1 teaspoon of vanilla extract until just combined. Scrape down the sides of the bowl.
In a separate bowl, whisk together the flour, baking powder, salt, and finely ground Earl Grey tea leaves.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until a soft dough forms. Do not overmix.
Wrap the dough in plastic wrap and chill in the refrigerator for at least 30 minutes. Chilling helps prevent spreading.
Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper.
Scoop the dough using a tablespoon measure or a small cookie scoop. Roll into balls and place them 2 inches apart on the prepared baking sheets. Gently flatten each ball slightly with the bottom of a glass.
Bake for 10 to 12 minutes, or until the edges are set and lightly golden. The centers should still look slightly soft.
Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
While cookies cool, prepare the glaze: Whisk together the powdered sugar, milk, and 1/2 teaspoon of vanilla extract until smooth. Add more milk, a drop at a time, if the glaze is too thick.
Once cookies are completely cool, drizzle or dip the tops into the vanilla glaze. Let the glaze set before serving.
Notes
For the best Earl Grey flavor, use high-quality loose-leaf tea and grind it very finely using a spice grinder or food processor until it resembles powder.
If you prefer a shortbread texture, reduce the baking time by 1-2 minutes and use only granulated sugar instead of brown sugar.
You can add 1/4 teaspoon of dried culinary lavender to the dough with the dry ingredients for a true London Fog experience.