In a large bowl, combine warm milk and yeast. Let sit for 5–10 minutes until foamy. Add sugar, eggs, and melted butter, mixing until smooth. Gradually add flour and salt, mixing to form a soft dough. Knead for 5–7 minutes until smooth and elastic. Cover and let rise in a warm place for 1 hour, or until doubled in size.
In a small bowl, mix softened butter, brown sugar, and all chai spices until a smooth paste forms. Set aside.
Roll out the dough on a floured surface into a large rectangle (about 16x12 inches). Spread the chai filling evenly over the dough. Roll tightly from the long side into a log, then slice into 12 equal rolls. Place in a greased 9x13-inch baking dish. Cover and let rise for 20–30 minutes.
Preheat oven to 350°F (175°C). Bake rolls for 22–25 minutes, or until golden brown. While they cool slightly, whisk together glaze ingredients until smooth. Drizzle over warm rolls before serving.