Preheat the oven to 350 degrees F (175 degrees C). Grease two 6-inch round springform pans.

Combine sugar, oil, and eggs in a large mixing bowl and mix well.

Sift flour, baking soda, baking powder, cinnamon, nutmeg, salt, cloves, and ginger into a separate bowl; stir into sugar mixture. Stir in pumpkin until well blended. Pour batter evenly into the prepared pans.

Bake in the preheated oven until a toothpick inserted into the center of each cake layer comes out clean, 45 to 55 minutes. Turn out onto wire racks to cool completely, about 30 minutes.

Cut rounded tops off of cooled cakes with a large, serrated bread knife so they are flat and even.

Combine powdered sugar, cream cheese, butter, and vanilla extract in a large mixing bowl. Whip until there are absolutely no lumps; this may take up to 5 minutes. Set aside.

Place 1 tier of cake onto a serving plate. Frost the top liberally; place second tier on top. Generously frost the entire cake. Stick almonds gently by the handful onto the sides of the cake.