Preheat oven to 350.
Using a stand mixer, blend yellow cake mix, vanilla pudding mix, and oil. Add eggs one at a time, mixing briefly between additions.
In a glass measuring cup or coffee mug, warm 1 c of water in microwave for about 30 seconds (until it's hot enough that it's producing steam). Add chai tea bag to water and allow to steep for about 3 minutes.
Pour tea into cake batter and continue to mix until fully blended.
In a separate bowl, mix brown sugar, cinnamon, and ground cloves. Set aside.
Pour half of the cake batter into a greased bundt cake pan. Sprinkle half of the brown sugar mixture evenly across the batter.
Pour remaining half of cake batter over brown sugar mixture, and then sprinkle the remaining half of the sugar mixture on the cake batter. So, you'll end up having 2 layers of cake batter and two layers of brown sugar mixture - one sugar mix in the middle and one on the bottom of the cake.
Place bundt cake pan in oven and bake for 20 minutes at 350. After 20 minutes, reduce the oven temperature to 325 and continue baking an additional 35-40 minutes.
Remove cake from oven and set cake pan on a rack to begin cooling.
While the cake is beginning to cool, you can quickly whip up the glaze. Start by pouring milk into a microwave-safe bowl and heat in microwave for about 10-20 seconds - until the milk is warm. Place chai tea bag in milk and allow it to steep for about 3 minutes. After 3 minutes, remove tea bag from milk, press tea bag to drain liquid from the bag into the bowl, and then whisk in vanilla and powdered sugar into the bowl.
Once the glaze is fully mixed (it will be very liquid-y - that's normal!), remove the cake from the bundt cake pan and set on a platter or plate. It'll still be quite warm - that's a good thing! Quickly poke holes with a toothpick throughout the top and sides of the cake - you won't see the holes, but they'll help the glaze seep into the cake.
Drizzle glaze evenly across the cake. You won't see the glaze except for the part that runs off onto the plate. However, I promise you'll taste it, and it'll be delicious!
Sprinkle cake with a tiny bit of powdered sugar just before serving - helps to give it a little pop of color and garnish!
Serve with coffee or with a scoop of vanilla ice cream. Enjoy with people around your table!