Substituting goat cheese for the standard cream cheese gives this frosting an extra-tangy kick.
Prepare Cake: Preheat oven to 350°. Grease 2 (8-inch) round cake pans; line bottoms with parchment paper, and grease and flour paper.
Stir together flour and next 3 ingredients.
Whisk together sugar and oil in a large bowl until well blended. Add eggs, 1 at a time, whisking until blended after each addition. Add flour mixture, stirring just until blended. Fold in carrots and next 3 ingredients. Spoon batter into prepared cake pans.
Bake at 350° for 40 to 45 minutes or until a wooden pick inserted in center comes out clean. Cool in pans on wire racks 15 minutes. Remove from pans to wire racks; discard parchment paper. Cool completely (about 1 hour).
Prepare Frosting: Beat goat cheese and butter at medium speed with an electric mixer 2 to 3 minutes or until creamy. Add powdered sugar, 1 cup at a time, beating at low speed until blended after each addition.
Split vanilla bean; scrape seeds into goat cheese mixture. Beat 30 seconds to 1 minute or until frosting is light and fluffy. Spread 1/2 cup frosting between cake layers; spread remaining frosting on top and sides of cake.