Brown the butter over medium heat until foamy, nutty, and golden. Transfer to a bowl and chill in the freezer for 10 to 15 minutes until firm but scoopable.
Grind the chai tea bags into a fine powder.
Cream the chilled brown butter with the coconut sugar and granulated sugar for about 90 seconds, starting on low speed and increasing to high. Add the eggs one at a time, then add the vanilla and miso and mix just until combined.
Add the ground chai, cinnamon, cardamom, nutmeg, and ginger and mix lightly.
Add the all purpose flour, oat flour, cornstarch, baking soda, and salt. Mix on low speed until just combined. Do not overmix. Fold in the chocolate chunks.
Chill the dough for 15 to 20 minutes. Scoop into rough 6 ounce dough balls, keeping the edges uneven. Place four cookies per baking sheet.
Bake at 410°F for 10 to 13 minutes, until the tops are matte, the edges are set, and the centers are still gooey. Let the cookies cool on the baking sheet for 30 minutes.
Whisk together the powdered sugar, chai concentrate or milk, cinnamon, cardamom, and vanilla until smooth. Drizzle over warm cookies.
