In a large mixing bowl or the bowl of a stand mixer, use a mixer to cream the butter with 1 cup of the granulated sugar and the brown sugar until light.
Add in the egg and the vanilla extract.
In a separate mixing bowl, sift or whisk the all-purpose flour, baking soda, salt 1/4 teaspoon of the allspice and 1 teaspoon of the cinnamon.
Alternate adding the sifted dry ingredients to the batter with the buttermilk, beginning and ending with the dry ingredients; only mix until just combined after each addition. Fold in the chopped rhubarb.
Spread 2/3 of the batter into a greased Bundt pan. Combine the remaining sugar, allspice and ground cinnamon. Sprinkle on top of the batter in the Bundt pan; add remaining batter over the top of the sugar mixture.
Bake for 1 hour at 350°F, or until a toothpick inserted in the middle of the cake comes out clean.
Leave cake in Bundt pan 10-15 minutes, then release cake onto a wire rack to cool completely.
Once cooled, combine glaze ingredients and add enough water to make a thick glaze. Drizzle over cake before serving.