Infuse the milk: Heat the milk until steaming but not boiling. Add chai tea bags, steep for 10 minutes, then remove bags and let the milk cool completely.
Prepare the pans: Preheat oven to 350°F (175°C). Grease and flour two 8-inch round or square cake pans.
Mix dry ingredients: In a large bowl, whisk flour, sugar, baking powder, baking soda, salt, and all spices until evenly combined.
Reverse cream: Add softened butter to the dry mixture and beat until it resembles coarse sand.
Add wet ingredients: Whisk eggs, vanilla, and cooled chai milk together. Gradually add to the batter, mixing on medium speed until smooth.
Bake: Divide batter evenly between pans. Bake for 30–35 minutes, or until a toothpick inserted in the center comes out clean.
Cool: Let cakes cool in pans for 10 minutes, then turn out onto a rack to cool completely.
Make frosting: Beat butter until creamy. Add powdered sugar gradually, then vanilla bean paste and cream. Beat until light and fluffy.
Assemble: Frost one layer, stack the second on top, then frost the top and sides evenly.