Preheat your oven to 350°F (175°C). Grease and line a 9x9 inch baking pan with parchment paper.

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

In a large mixing bowl, cream butter with granulated sugar and brown sugar until light and fluffy.

Add eggs one at a time, mixing well; then add vanilla extract and beat until smooth.

Gradually mix in buttermilk and dry ingredients alternately until just combined.

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

Cool in the pan for 30 minutes, then transfer to a wire rack to cool completely.

Prepare the frosting by browning the unsalted butter and mixing with cream cheese and powdered sugar until fluffy.

Make the chai milk soak by heating whole milk, steeping the chai teabags, and mixing with sweetened condensed milk.

Poke holes in the cooled cake and slowly pour the chai milk soak over it. Frost the top with the brown butter cream cheese frosting.

Sprinkle ground cinnamon on top, cut into squares, and serve.