Preheat oven to 350°F (180°C). Line bottom of a 9-inch springform pan with parchment paper; lightly spray sides of pan with baking spray with flour. In a large bowl, whisk together flour, baking powder, cinnamon, salt, baking soda, ginger, and cloves. In a medium bowl, whisk together sugar, applesauce, buttermilk, oil, eggs, and vanilla. Pour sugar mixture into flour mixture, and fold until well combined. Pour batter into prepared pan, smoothing top with an offset spatula. Bake until a wooden pick inserted in center comes out clean, 35 to 40 minutes. Let cool in pan for 10 minutes. Remove from pan, and let cool completely on a wire rack. Spread Vanilla Bean Frosting on cooled cake.
Vanilla Bean Frosting
In the bowl of a stand mixer fitted with the paddle attachment, beat cream cheese at medium-low speed until smooth, about 2 minutes. Add butter, and beat until smooth, about 2 minutes. Add confectioners’ sugar, 1 cup (120 grams) at a time, beating well after each addition. Increase mixer speed to medium-high. Add vanilla bean paste and salt. Increase mixer speed to medium-high, and beat for 2 minutes. Use immediately.