Preheat oven to 425°F (220°C). Line a baking sheet with parchment paper.

For the cake: Rinse and dry sweet potatoes. Place on prepared pan.

Bake until soft and easily pierced with a fork, 30 to 45 minutes. Let cool enough to handle.

Remove skin, and place potato flesh in a large bowl. Let cool completely, 1 to 2 hours. Mash potatoes.

Preheat oven to 350°F (180°C). Spray 3 (8-inch) round cake pans with baking spray with flour.

In a large bowl, whisk together flour, cinnamon, baking powder, baking soda, salt, ginger, nutmeg, cloves, and allspice.

In the bowl of a stand mixer fitted with the paddle attachment, beat butter, granulated sugar, brown sugar, and oil on medium speed until well combined and smooth, about 5 minutes. Scrape down sides of bowl. Add eggs, one at a time, ensuring each egg is fully incorporated prior to adding the next, 20 to 30 seconds each. Scrape down sides of bowl. Add mashed sweet potato and vanilla extract, beating until combined, 30 seconds to 1 minute. (The batter may break but will come back together soon.) Add flour mixture, and continue to beat until combined and smooth, about 1 minute. Scrape down sides of bowl. Continue to beat for 10 to 15 seconds. Fold in carrots. Divide batter among prepared pans.

Bake until a wooden pick inserted in center comes out clean, 25 to 30 minutes. Let cool in pans for 10 minutes. Remove from pans, and let cool completely on wire racks.

For the frosting: In the bowl of a stand mixer fitted with the paddle attachment, beat butter on medium speed until fluffy and lighter in color, about 2 minutes. Add cream cheese, and continue to beat until fluffy and combined, about 2 minutes. Add confectioners’ sugar, meringue powder, vanilla extract, and salt, and continue to beat until combined and smooth, 2 to 3 minutes. Scrape down sides of bowl. Continue to beat for 30 seconds to 1 minute.

Place 1 cooled cake layer on a cake stand. Dollop with a generous amount of frosting, and spread evenly. Repeat with remaining 2 cake layers and frosting, and stack layers. Spread remaining frosting on top and sides of cake.