Cream 1 cup unsalted butter (make sure it's cold), 2 teaspoons chai tea leaves, 1 teaspoon ground cinnamon, ½ teaspoon ground cardamom, ½ teaspoon salt, ¼ teaspoon ground ginger, ⅛ teaspoon ground clove, and ⅛ teaspoon ground allspice together in the bowl of a stand mixer fitted with a paddle attachment.
Add in ½ cup powdered sugar and mix until incorporated.
Add in 2 cups all-purpose flour a little at a time and mix for about 4 to 5 minutes until a soft Play-Doh-like dough forms. The mix will be dry and crumbly at first but will come together after several minutes.
Transfer the dough to a large piece of parchment paper and shape and roll it into a log using the parchment paper to help you. The log should be about 11.5 to 12 inches long and 2 in diameter.
Chill the dough log for at least 4 hours, preferably overnight or for several days. The flavor increases the longer this dough chills.
When ready to bake, preheat the oven to 350°F and line a baking sheet with parchment paper.
Use a very sharp knife to cut the log into 24 cookies (just under .5-inch wide slices for each) and place them 1 inch apart on the prepared baking sheet. I like to roll the bottom of the cut slices on the pan to smooth out any frays from the cut and shape them to be more rounded if needed.
Bake for 14 to 16 minutes or until the edges are golden brown.
Allow the cookies to cool on the pan for a few minutes before transferring to a cooling rack to cool completely.
Once cooled, whisk together 1 cup powdered sugar, 1 tablespoon heavy cream2 teaspoons vanilla extract, and ¼ teaspoon ground cinnamon until smooth.
Dip the top of each cookie in the icing, let excess drip off and run a spoon along the edge to remove any extra, then place on wax paper to set until the icing hardens.