Cream the butter, oil, granulated sugar, powdered sugar, egg, and vanilla in a large mixing bowl.
Slowly fold in the crushed-up chair tea leaves and mix well.
Slowly fold in the flour, baking soda, and salt, and mix well. Scrap the sides of the bowl to absorb all of the dry ingredients.
Divide the dough into two equal portions and shape each into a disk.
Wrap the dough disks in plastic wrap and refrigerate for at least 1 hour or until firm.
Preheat your oven to 350 degrees F (175°C)—line baking sheets with parchment paper.
On a lightly floured surface, roll out one portion of the dough to about 1/4 inch thickness. Use cookie cutters to cut out desired shapes and place them on the prepared baking sheets.
Bake in the preheated oven for 8-12 minutes or until the edges are lightly golden.
Allow the cookies to cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely. Repeat with the remaining dough. Drizzle with the glaze, and sprinkle some granulated sugar on top.