Heat the milk in a saucepan with the teabags or loose-leaf tea over low heat until it starts to simmer. Once simmering, turn the heat off and let the tea steep in the milk as it cools.
Once it has cooled and you are ready to start baking, pass the milk through a fine mesh strainer to remove any tea.
Preheat the oven to 350°F / 180°C and grease two 8-inch cake pans.
In a bowl, beat together the butter and both sugars until light and fluffy.
Add the eggs, one at a time, beating in between each addition.
Add the vegetable oil, sour cream and vanilla and mix until combined.
In a separate bowl, mix together the dry ingredients, including flour, baking powder, baking soda, salt, pepper, cardamom, cinnamon, ginger and nutmeg.
Add a third of the flour mixture to the cake batter and mix it in slowly.
Once the flour is totally incorporated, add half of the steeped chai tea and mix that in completely.
Repeat with another third of the flour, the remaining milk, and then the remaining flour, making sure to mix in completely after each addition.
Divide the cake batter evenly between the prepared cake pans and bake for 35-40 minutes, or until a skewer comes out clean.
Let cool completely in the cake pans. If you are making the brown butter frosting to go with it, I recommend starting the brown butter now (or even before baking the cake), so it will be ready to use once the cakes have cooled).
Once cooled, cut the dome off of the cakes. If you would like two layers of cake, leave it as is. If you would prefer four thinner layers (as in the photographs above), cut each layer in half. Tip: I like to use a cake leveler to ensure even cuts!
Make the Brown Butter Cream Cheese Frosting
It's best to brown the butter ahead of time so it will be sufficiently cooled and ready to use when you want to make the frosting.
Start by putting the butter in a medium saucepan over medium heat, let it start to melt. As your butter begins to heat, it will froth up and start to bubble and make crackling noises - this is the water boiling out of the butter.
After the crackling subsides a little, the butter will start to change in color very quickly so keep an eye on it. Once you start to smell a lovely nutty aroma, and the butter has browned in color, it is ready. Take it off the heat and transfer it to a bowl to cool and thicken- don't miss out on those lovely brown bits in the bottom - those are the milk solids and they are what brings the flavor!
Once the brown butter is the consistency of regular room temperature butter, mix it all together to disperse the milk solids evenly throughout the brown butter.
Add the brown butter to the bowl of a mixer with the cream cheese and beat together until combined and smooth.
Sieve the powdered sugar to remove any lumps, then mix it into the cream cheese mixture gradually and slowly.
Once all the icing sugar is in, add the vanilla and salt, then turn the mixer on high for 1 minute.
Consistency can vary depending on room temperature, measuring methods etc, so you may need more or less powdered sugar. If you would like the frosting to be thicker, add another cup of powdered sugar. If you would like it to be thinner, add a little dash of milk.
Notes
When steeping the chai tea in the milk, do not let the milk boil. As soon as you see it start to simmer, remove it from the heat. I have found similar results using both chai teabags and loose-leaf chai tea - whatever your preference is will work just fine. Just make sure you strain out any tea from the milk before adding it to the cake! It's best to make the brown butter ahead of time so it can cool and harden sufficiently before you need to use it.