Preheat your oven to 350 degrees F. Grease a 9-inch round springform cake pan, or a normal 9-inch round cake pan with at least 2-inch high sides.
In a medium bowl, whisk the dry ingredients: flour, baking powder, salt, ginger, cinnamon, nutmeg, and cloves. Set aside.
In a large microwave-safe bowl (I use a large glass bowl), or on the stove, melt the butter. Let it sit for a couple minutes to cool, then whisk in the brown sugar, followed by the eggs one at a time, then the Greek yogurt and vanilla, until combined and smooth.
Dump the dry ingredients into the bowl with the wet ingredients and stir together until well-combined and no lumps remain.
Fold in the grated parsnips and chopped walnuts until evenly distributed.
Pour the batter into the prepared pan, smooth out the surface, and bake for 50-55 minutes, or until cake springs back when touched and a tester inserted in the center comes out clean.
Let cake cool in pan on a rack for 10 minutes, then remove the sides of the springform pan to release the cake. Let cake cool completely while you prepare the frosting.
For the Cream Cheese Frosting:
In a large bowl using a stand mixer with the whisk attachment, or a hand mixer, beat cream cheese and butter at high speed until pale and very fluffy - this should take 2-3 minutes. You want to incorporate as much air as possible into the mixture to make it light and fluffy. Add the powdered sugar, vanilla, and salt, and beat at medium to high speed until fully combined and light.
Spread cooled cake with cream cheese frosting. It should make a thick layer, and can be swirled in pretty patterns with an offset spatula.
Decorate the outer edges of cake with sugared cranberries and additional chopped walnuts if desired. Serve!
Cake will keep, well-wrapped in the fridge, for up to 4 days. I like to microwave leftover pieces of cake on 50% power for 20 seconds to reheat.*I grated the parsnips by hand using a box grater, which sounds like a lot of work but doesn't actually take all that long, since you only need about 2 parsnips to get 2 cups worth of grated parsnips. You can also grate them in a food processor with a grating blade.Recipe adapted, somewhat generously, from my single-layer carrot cake.
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