Step 1

Cook sweet potatoes in a medium pot of boiling water, stirring occasionally, until a tester inserted into centers meets no resistance, 40–45 minutes. Drain and let sit until cool enough to handle. Remove skins, transfer flesh to a medium bowl, and mash with a potato masher or fork. Let cool.

Step 2

Preheat oven to 350°. Spray three 9"-diameter cake pans with nonstick spray, then line bottoms with parchment paper rounds. Spray parchment and dust pans with flour, tapping out excess.

Step 3

Sift baking powder, cinnamon, nutmeg, salt, and 3¼ cups (374 g) cake flour into a large bowl (or just whisk to remove lumps). Combine granulated sugar, brown sugar, butter, oil, and vanilla in the bowl of a stand mixer fitted with the paddle attachment. Beat on medium-high speed until light, fluffy, and no lumps remain, about 5 minutes.

Step 4

Add eggs to sweet potato purée and mix well. Scrape into sugar mixture and beat to combine, scraping down bowl as needed. Reduce speed to low and with motor running, gradually add dry ingredients; mix just until incorporated. Divide batter evenly among prepared pans. Bake until cakes are slightly risen, tops are set, and a tester inserted into the centers comes out clean, 25–30 minutes.

Step 5

Transfer pans to a wire rack and let cakes cool in pans 5 minutes. Run a small knife around edges of cakes and turn out onto racks. Remove parchment and let cool completely (rounded side down). Tightly wrap cakes individually in plastic and freeze until thoroughly chilled (this will make cakes easier to frost), about 2 hours.

Step 6

Beat cream cheese and butter in the bowl of a stand mixer fitted with paddle attachment on high speed until smooth and creamy, about 1 minute. Add powdered sugar, vanilla, and salt and beat on low speed 30 seconds (place a kitchen towel over bowl to capture any puffs of sugar). Increase speed to high and beat frosting 2 minutes. It should be thick and creamy.

Step 7

Place a cake, right side up, on a large plate or cake stand. Spread one third of frosting on top. Set another cake on top and frost with half of remaining frosting. Repeat process with remaining cake and frosting. For the cleanest slices, chill 3 hours before slicing. Top with orange zest strips just before serving if desired.