Preheat the oven to 350°F. Prepare three 6-inch or two 9-inch cake pans by spraying the sides with a cooking spray (Baker's Joy is my favorite) and fitting a wax or parchment paper circle to the bottom of the pan. Alternatively, you can grease and lightly flour the pans.
Place the chai tea bag into a mason jar. In a small saucepan over medium-high heat, warm the whole milk, stirring constantly, until it begins to boil. Pour the boiling milk over the chai tea bag in the mason jar and let steep for 20 minutes before removing the tea bag. Allow the mixture to cool completely to room temperature before moving on.
Sift the cake flour and then measure by spooning and leveling it in your measuring cup. Add the cake flour, baking powder, baking soda, 4 teaspoons of the chai spice mix, and salt into a bowl and whisk to combine. Set aside.
In the bowl of your stand mixer (a handheld mixer works fine too!), cream the butter for on high for two minutes until it's light and fluffy. Add in sugar and continue to mix on medium-high for another two minutes, scraping down the bowl and paddle as needed. Add the eggs one at a time, then add vanilla and sour cream and mix for one minute on high, scraping down the bowl and paddle once more.
With the mixer on low speed, add in the dry ingredients and mix until just combined. Add the (room temperature!) chai milk mixture slowly and mix until just incorporated. Scrape down the sides and bottom of the bowl and give it a few stirs to make sure there are no lumps (without over-mixing). The batter will be slightly thick, but pourable.
Pour batter evenly into prepared cake pans (no more than 2/3 of the way full) and bake for 30-35 minutes. They're done when they spring back to the touch and a toothpick inserted into the middle comes out clean. Let the cakes cool in the pan for five minutes before turning them out onto a wire rack for an additional few hours of cooling. Make sure they're entirely room temperature before applying any frosting.