Step 1: Preheat your oven to 350°F (175°C) and grease a 9×13 inch baking pan or two 8-inch round cake pans.
Step 2: Heat the milk in a small saucepan or microwave until steaming. Steep the chai tea bags in the milk for 10 minutes, then squeeze the bags and discard. Let the milk cool.
Step 3: In a medium bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon, ginger, cardamom, and cloves.
Step 4: In a large bowl, cream the butter, granulated sugar, and brown sugar together until light and fluffy (about 3-5 minutes).
Step 5: Beat in the eggs one at a time, followed by the vanilla extract and pumpkin puree.
Step 6: Gradually add the dry ingredients to the wet ingredients, alternating with the chai-infused milk, beginning and ending with the dry ingredients.
Step 7: Pour the batter into the prepared pans and bake for 35-45 minutes, or until a toothpick inserted into the center comes out clean.
Step 8: Allow the cake to cool completely in the pan on a wire rack before frosting.
Step 9: To make the frosting, beat the cream cheese and butter until smooth. Add the powdered sugar and chai spice blend, beating until light and airy. Spread over the cooled cake.