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In the bowl of an electric mixer, fitted with a paddle, combine the 1/2 cup of the butter, oil, sugar, and brown sugar. Cream the mixture until smooth.
Sift the flour, baking powder, baking soda, 1 teaspoon cinnamon, and salt into a small mixing bowl. Add the egg to the butter/sugar mixture, one at a time. Add the flour mixture to the butter/sugar mixture, 1/2 cup at a time. Add the parsnips, ground walnuts and vanilla. Mix well. Pour the batter into the prepared pans and spread evenly. Place in the oven and bake for about 30 to 40 minutes or until the center sprigs back when touched. Remove from the oven and cool.
In the bowl of an electric mixer, combine the cream cheese and remaining 1/2 cup butter. Mix well. Add the walnut pieces and remaining 1 teaspoon cinnamon. Mix well. Add the powdered sugar, 1 cup at a time and mix until the frosting is spreadable.
To assemble, slice each cake in half. Place on half in the center of a serving plate. Brush the top of the cake with the simple syrup. Spread 1/2 cup of the frosting over the first layer. Repeat the above process until all of the layers are used. Ice the entire cake with the remaining frosting. Refrigerate the cake for 30 minutes. Slice the cake and serve.