How to Make It
Preheat oven to 350°F.
To prepare cake, cut thin ends of parsnips into 3/4-inch pieces. Cut wide ends of parsnips lengthwise into quarters. Cut out and discard core from each piece; cut pieces into 3/4-inch pieces. Place parsnips on a foil-lined baking sheet. Drizzle with 1 tablespoon oil; toss to coat. Bake at 350°F for 25 minutes or until tender. (Leave oven on.) Place parsnips in a mini food processor with 1/4 cup water; process until smooth. Cool slightly.
Weigh or lightly spoon flour into dry measuring cups; level with a knife. Whisk together flour and next 5 ingredients (through nutmeg). Place remaining 7 tablespoons oil, 3/4 cup brown sugar, 1 teaspoon vanilla, and eggs in a large bowl; beat with a mixer at medium speed until well combined (about 2 minutes). With mixer on low speed, gradually add flour mixture and buttermilk alternately to oil mixture, beginning and ending with flour mixture. Add parsnips; beat just until combined. Spread batter into a 13- x 9-inch light-colored metal baking pan coated with cooking spray. Bake at 350°F for 25 minutes or until a wooden pick inserted in center comes out clean. Cool completely in pan.
To prepare icing, place butter and cream cheese in a large bowl; beat with a mixer at medium speed until smooth. Add powdered sugar, 1/3 cup brown sugar, 1/2 teaspoon vanilla, and 1/4 teaspoon salt; beat just until combined. Spread icing over cake; sprinkle with pecans.