Preparation Preheat oven to 350°F. Butter and flour 13x9x2-inch baking pan. Combine flour, sugar, ground ginger, baking powder, cinnamon, 3/4 teaspoon salt, nutmeg, allspice, and cloves in large bowl; whisk to combine. Whisk eggs, oil, milk, and 1 teaspoon vanilla in medium bowl to combine. Pour egg mixture over dry ingredients; stir until just combined. Stir in parsnips and walnuts. Transfer batter to prepared pan. Bake until tester inserted into center comes out clean, about 25 minutes. Cool cake completely in pan on rack. Beat cream cheese and butter in large bowl until smooth. Beat in fresh ginger and remaining 1/8 teaspoon salt and 1/2 teaspoon vanilla. Gradually add powdered sugar and beat until frosting is smooth. Spread over cake. (Can be prepared 1 day ahead. Cover and chill.)
Preparation Preheat oven to 350°F. Butter and flour 13x9x2-inch baking pan. Combine flour, sugar, ground ginger, baking powder, cinnamon, 3/4 teaspoon salt, nutmeg, allspice, and cloves in large bowl; whisk to combine. Whisk eggs, oil, milk, and 1 teaspoon vanilla in medium bowl to combine. Pour egg mixture over dry ingredients; stir until just combined. Stir in parsnips and walnuts. Transfer batter to prepared pan. Bake until tester inserted into center comes out clean, about 25 minutes. Cool cake completely in pan on rack. Beat cream cheese and butter in large bowl until smooth. Beat in fresh ginger and remaining 1/8 teaspoon salt and 1/2 teaspoon vanilla. Gradually add powdered sugar and beat until frosting is smooth. Spread over cake. (Can be prepared 1 day ahead. Cover and chill.)