Spiced Applesauce Cake

adapted from Smitten Kitchen
For cake
3 cups (13.5 ounces) all-purpose flour
3 teaspoons baking powder
3/4 teaspoon baking soda
3/4 teaspoon salt
1 teaspoon cinnamon
3/4 teaspoon ground ginger
1/2 teaspoon ground cardamom
1/4 teaspoon ground cloves
1 1/2 stick (6 ounces) unsalted butter, softened
1 1/2 cup packed light brown sugar
1 1/2 teaspoon vanilla extract
3 large eggs
2 1/4 cups unsweetened applesauce

For frosting
8 ounces cream cheese, softened
5 tablespoons unsalted butter, softened
1/2 teaspoon pure vanilla extract
1 1/2 cup (6 ounces) confectioners sugar
3/4 teaspoon cinnamon

Preheat oven to 350°F with rack in middle. Butter a 9 x 13-inch cake pan. If you don’t have a nonstick cake pan or are a little nervous, line the bottom with parchment paper and butter that too.

Make cake: Whisk together flour, baking powder, baking soda, salt, and spices. Beat butter, brown sugar, and vanilla with an electric mixer at high speed until pale and fluffy, 2 to 3 minutes. Add eggs one at a time, beating well after each addition, then beat in applesauce. At low speed, mix in flour mixture until just combined. The batter will look a little curdled and uneven but it will bake up perfectly.

Spread batter evenly in pan and bake until golden-brown and a wooden pick inserted into center comes out clean, about 35 to 40 minutes. Cool in pan 15 minutes. Run a knife around edge of cake to loosen, then invert onto a plate. Re-invert cake onto a rack to cool completely.

Make frosting: Beat cream cheese, butter, and vanilla with an electric mixer at high speed until fluffy. Sift confectioners sugar and cinnamon over cream cheese mixture, then beat at medium speed until incorporated. Spread frosting over top of cooled cake.

Do ahead: kept for three days . Keep frosted cake in the fridge. If you’d like to bake the cake further in advance, wrap it well and freeze it until the day you need it. Leave it out on the counter to defrost and frost it up to a day in advance.