1. Preheat oven to 350°F (175°C). Grease and line a 9×9-inch baking pan.

2. Mix dry ingredients:
   In a medium bowl, whisk together flour, spices, baking powder, baking soda, and salt.

3. Cream butter and sugars:
   In a large bowl, beat butter, granulated sugar, and brown sugar until light and fluffy.

4. Add eggs and vanilla:
   Mix in eggs one at a time, then add vanilla extract.

5. Combine wet and dry:
   Add dry ingredients alternately with buttermilk, stirring just until smooth.

6. Bake:
   Pour into prepared pan and bake for 35–38 minutes, or until a toothpick comes out clean. Cool completely.

Make the chai milk soak:

1. Heat milk until steaming; steep tea bags for 20 minutes. Cool.

2. Stir in sweetened condensed milk and vanilla extract.

Make the frosting:

1. Brown the butter in a saucepan until golden and nutty; chill until firm but spreadable.

2. Beat brown butter until fluffy. Add cream cheese and beat until smooth.

3. Add powdered sugar and beat until light and spreadable.

Assemble the cake:

1. Trim cake top if needed. Poke holes all over the surface.

2. Slowly pour chai milk soak evenly over the cooled cake.

3. Once absorbed, spread cream cheese frosting over the top.

4. Dust with cinnamon and cut into squares to serve.