I do not know if my considerable fondness for this cake stems from the quantity of parsnips hidden within it or because those parsnips have been subsumed into a greater whole, a toothsome cake with an appealing but hard-to-pinpoint flavor. Regardless, it’s a winner.
Make the buttercream: Pour the blood orange juice into a small saucepan and bring to a boil. Cook until reduced by half and syrupy, about 10 minutes. Remove from the heat and let cool completely.
In a stand mixer fitted with the paddle attachment, cream the butter on medium-high until fluffy, about 2 minutes. Stop the machine, add the reduced blood orange juice, and beat to incorporate. Incorporate the confectioners’ sugar into the creamed butter 1 cup at a time—stop the machine, add it, slowly stir it in, increase the speed to really beat it, then stop and repeat. This is not a don’t-overwork-it thing, this is a keep your-kitchen-from-looking-like-a-wig-powdering-room thing.
Make the cake: Heat the oven to 350°F for cake or 375°F for cupcakes. Grease a 13 × 9-inch pan,
two 9-inch round cake pans, or line 18 cups of a muffin tin with paper liners.
Whisk together the eggs, granulated sugar, oil, milk, salt, and vanilla in a large bowl until smooth. Stir in the flour, baking powder, cinnamon, nutmeg, allspice, and ground cloves and stir together with the whisk until smooth and homogenous, about 2 minutes. Fold the parsnips and ginger into the cake batter.
Pour the batter into the greased pan(s)—this batter isn’t going to grow much in the oven, so fill the cake pan(s) or cupcake liners to within a half inch of the top. Bake until a toothpick inserted into the center of the cake or cupcake comes out clean, about 24 minutes for cake, 16 minutes for
cupcakes. Let cool for 10 minutes, then remove whatever you’ve baked from whatever it was
baked in, and cool completely on a rack before frosting.