Step 1Make almond powder by grinding the almonds in a food processor until they become grainy like sand, about 30 seconds. Do not over-process or the mixture will turn into a paste. Set aside.
Step 2Beat the butter in the bowl of an electric mixer on medium-high speed until it looks creamy, 1 minute, scraping the bowl once with a rubber spatula. Add the powdered sugar and mix on low speed until the sugar is just incorporated into the butter, 30 seconds. Scrape the bowl. Increase the speed to medium-high and beat until the mixture is light and fluffy, 2 to 3 minutes. Scrape the sides of the bowl occasionally.
Step 3Meanwhile, in a separate bowl, combine the almond powder and the cake flour.
Step 4Add half of the egg yolks to the sugar-butter mixture and beat until well incorporated, about 15 seconds. Beat in the remaining yolks.
Step 5Add the dry ingredients to the wet mixture in 4 stages and mix on low speed until all the flour is well incorporated, about 2 to 3 minutes. Stir in the tea leaves.
Step 6Cover the dough with plastic wrap and refrigerate for 1 hour. Take the dough out of the refrigerator and mix with an electric mixer on low speed until the dough is softened a bit and easier to handle, about 30 seconds. On a lightly floured surface, roll the dough into 2 (12-inch) logs, 1 1/2 inches in diameter. Wrap the dough in plastic wrap and refrigerate for 2 hours or overnight.
Step 7Heat the oven to 350 degrees.
Step 8Slice the logs into 1/4-inch-thick cookies and place them 1/2 inch apart on baking sheets. Bake the cookies for 13 to 14 minutes, rotating the pans halfway through. The bottoms of the cookies should look golden brown when done. Let the cookies stand on the baking sheets for 2 to 3 minutes before transferring them to a rack to cool.