Preheat the oven to 350°F/177ºF. Prepare three 6-inch or two 8-inch cake pans by spraying the sides with a baking spray and fitting a parchment paper circle to the bottom of the pan.
Add the cake flour, baking powder, baking soda, ground Earl Grey tea, and salt into a medium bowl and whisk to combine. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter at high speed for about 2 minutes, until it is creamy. Add the sugar and mix the ingredients at medium-high speed for 2 minutes, scraping the bowl and paddle at the halfway point. Decrease the mixer’s speed to low and add the eggs, one at a time, mixing until they are just combined and scraping the bowl and paddle as needed. Add the sour cream and vanilla, increase the mixer’s speed to high and beat the ingredients for 1 minute.
With the mixer in the off position, add in the dry ingredients all at once. Turn the mixer to low speed and mix until just combined, then add the (room temperature!) Earl Grey milk mixture in a slow steady steam 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. The batter will be slightly thick.
Pour the batter evenly into the prepared cake pans 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.