Combine dry ingredients. In a large mixing bowl, whisk the flour, baking soda, salt, cinnamon, ginger, cardamom, and chai tea until combined. Set aside.
Combine the butter, oil and sugar. In a large mixing bowl or the stand mixer bowl with the paddle attachment, beat the butter on medium speed for 1 minute then add the vegetable oil, sugar, and powdered sugar and mix for an additional 2-3 minutes until light and fluffy. Scrape down the sides of the bowl to combine.
Add egg and vanilla. Then add the egg and vanilla and mix on medium speed until combined.
Combine dry ingredients. Next, slowly combine the dry ingredients on low speed until just combined. Scrape down the sides of the bowl and mix combine.
Chill. Cover and chill in the refrigerator for at least 30 minutes to 1 hour.
Prepare oven. Preheat the oven to 350 degrees F and place the oven rack in the center position. Line your baking sheets with parchment paper.
Scoop and cover in cinnamon sugar. In a small mixing bowl, mix the cinnamon and sugar. Using a cookie scoop, scoop the cookie dough. Roll each dough in the cinnamon sugar until covered.
Gently flatten the cookie dough. Place the cookie dough balls onto the parchment paper-lined baking sheet about 2 inches apart from each other. Using your palm or a flat-bottomed glass gently press down the dough balls until they are about 1/4 inch thick.
Bake. Bake each tray of cookies one at a time for 9-11 minutes or until lightly golden brown along the edges. Let the cookies cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.
Glaze. In a medium mixing bowl, mix the powdered sugar, milk, nutmeg, and cinnamon. When the cookies have cooled completely, spoon the glaze over the center. Enjoy!