Adjust oven rack to middle position and heat oven to 350 degrees. Grease 18 by 13-inch rimmed baking sheet, line with parchment paper, and grease parchment. Whisk flour, baking powder, baking soda, cinnamon, nutmeg, salt, and cloves together in large bowl.
Whisk sugar, oil, eggs, and vanilla together until mixture is smooth. Stir in carrots and currants. Add flour mixture and fold with rubber spatula until mixture is just combined.
Transfer batter to prepared baking sheet and smooth surface with offset spatula.
FOR THE FROSTING:
Using stand mixer fitted with paddle, beat butter, sugar, buttermilk powder, vanilla, and salt on low speed until smooth, about 2 minutes, scraping down bowl as needed. Increase speed to medium-low; add cream cheese, 1 piece at a time; and mix until smooth, about 2 minutes.
Transfer cooled cake to cutting board, parchment side down. Using sharp chef’s knife, cut cake and parchment in half crosswise and then lengthwise to make 4 equal rectangles, about 6 by 8 inches each.
Place 6 by 8-inch cardboard rectangle on cake turntable or plate. Place 1 cake rectangle, parchment side up, on cardboard and carefully remove parchment. Using offset spatula, spread 2/3 cup frosting evenly over cake layer. Repeat with two more layers of cake, frosting each layer with 2/3 cup frosting and pressing gently on each layer to level. Place last rectangle of cake on top and frost top of cake with 1 cup frosting. Use remaining frosting to coat sides of cake. (It’s fine if some crumbs show through frosting on sides, but if you go back to smooth top of cake, be sure that spatula is free of crumbs.)
Hold cake with 1 hand and gently press chopped pecans onto sides with other hand. Chill for at least 1 hour before serving.