Preheat the oven to 350°F. Grease a 9×9 inch light metal baking pan and line it with parchment paper.

In a medium bowl, whisk together the flour, cinnamon, ginger, allspice, nutmeg, cardamom, cloves, baking powder, baking soda, and salt. Set aside.

In a large bowl, cream together the softened butter, granulated white sugar, and brown sugar for 2 minutes with an electric mixer on high speed.

Add in the eggs and vanilla extract, mixing on medium speed until pale in color and smooth, about 1 minute.

Gradually add the buttermilk and dry ingredients, mixing on low speed until all is combined and the batter is smooth. Scrape the sides of the bowl as necessary.

Pour the batter into the prepared pan and bake for 35-38 minutes, or until a toothpick comes out clean from the center.

Let the cake cool in the pan on a wire rack for 30 minutes, then pull up on the parchment paper to release it from the pan. Let it continue cooling on the rack until completely cooled.

For the frosting, in a large pot, heat the butter over medium heat until it simmers. Simmer until the butter is foamy and has turned a deep golden brown, about 10-12 minutes. Transfer to a large bowl and allow it to cool in the fridge until solid but still soft.

Whip the brown butter on high speed with an electric mixer until pale and fluffy, 5-10 minutes. Add the cold cream cheese and mix on medium speed until fluffy.

Sift in the powdered sugar and mix on low speed until combined, then on high speed for 1 minute until fluffy again.

For the chai milk soak, heat the milk in a small saucepan over low heat until steaming. Add the teabags and allow to steep for 20 minutes, then remove and let cool.

Once cooled, mix the chai milk with the sweetened condensed milk and vanilla extract.

When the cake is completely cooled, cut a very thin layer off the top. Poke holes on the top of the cake using a wooden stick.

Slowly pour the chai milk mixture on top of the cake. Frost the top of the cake with a thick layer of brown butter cream cheese frosting. Sprinkle cinnamon on top, then cut into 16 slices and serve.