Preheat your oven to 350°F. Prepare a 9x9-inch light-colored nonstick pan with parchment paper and set it aside.
In a large bowl, whisk together the flour, baking soda, salt, cinnamon, ginger, nutmeg, allspice, and cloves.
In another bowl, combine the vegetable oil, eggs, brown sugar, granulated sugar, sour cream, and vanilla extract.
Pour the wet mixture into the dry ingredients and fold until just combined.
Incorporate the grated apples gently.
Transfer the batter to the prepared pan.
Bake for 35-40 minutes or until a toothpick inserted in the center comes out clean. Let the cake cool in the pan for 10 minutes before transferring it to a wire rack.
To make the brown sugar icing, melt the butter, dark brown sugar, and heavy cream in a medium saucepan over medium heat, whisking until combined and gently boiling.
Remove from heat and whisk in the vanilla extract and powdered sugar.
Pour the icing over the warm cake, letting it melt into the cake slightly.