Preheat oven to 350°F (175°C). Thoroughly grease a 12-cup Bundt pan.
Whisk together the flour, baking powder, cinnamon, cardamom, ginger, baking soda, salt, and pepper. Set aside.
Using an electric mixer on medium speed, beat the butter, sugar, and brown sugar until light and fluffy. Add the eggs, one at a time, mixing well after each addition. Mix in the vanilla.
Reduce the mixer speed to low. Mix in the flour mixture in three portions, alternating with two portions of buttermilk. Mix just until combined.
Transfer the batter to the prepared pan, and spread evenly.
Bake 55 to 60 minutes, or until a pick inserted into the center comes out clean. Cool the cake in the pan for 20 minutes. Then invert the pan onto a cooling rack or serving plate to cool completely.
To make the glaze:
Place the confectioners' sugar, 3 tablespoons (45ml) of cream, and the vanilla in a small bowl. Stir to combine. If necessary, add more cream, about a teaspoon at a time, until the glaze is the desired consistency.
Dollop the glaze on top of the cooled cake, allowing the glaze to spread down the sides of the cake.