Preheat the oven: to 350°F (175°C). Grease and flour a 9-inch round baking pan.
Prepare the cake batter:
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, ginger, cardamom, cloves, and nutmeg.
In a large bowl, beat the butter and brown sugar together until light and fluffy.
Add the eggs, one at a time, beating well after each addition. Mix in the vanilla extract.
Gradually add the dry ingredients to the wet ingredients, alternating with the buttermilk, beginning and ending with the dry ingredients. Mix just until combined.
Bake: Pour the batter into the prepared baking pan and spread it evenly. Bake for 25-30 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Make the chai spice syrup: While the cake is baking, combine the water, brown sugar, cinnamon, ginger, cardamom, cloves, and nutmeg in a small saucepan. Bring to a boil, then reduce the heat and simmer for 5 minutes. Remove from heat and let cool slightly.
Soak the cake: Once the cake is done, let it cool in the pan for 10 minutes. Poke holes all over the cake with a skewer or toothpick, then slowly pour the chai spice syrup over the top, allowing it to soak in.
Prepare the frosting: In a large bowl, beat the butter until creamy. Gradually add the powdered sugar, milk, vanilla extract, and cinnamon, beating until smooth and fluffy.
Finish the cake: Once the cake is completely cool, spread the frosting over the top.