Preheat oven to 350°F (175°C). Grease and flour a cake pan.
In a bowl, whisk together flour, baking powder, baking soda, salt, and chai spice blend.
In a separate bowl, cream together butter and sugar until light and fluffy. Beat in eggs one at a time, then stir in vanilla.
Gradually add the dry ingredients to the wet ingredients, alternating with buttermilk, beginning and ending with the dry ingredients. Mix until just combined.
Pour batter into the prepared pan and bake for 35-45 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes before inverting it onto a wire rack to cool completely.
For the frosting: In a bowl, beat together cream cheese and butter until smooth. Gradually add powdered sugar and beat until light and fluffy. Stir in ground ginger and heavy cream. Frost the cooled cake.