Preheat oven to 350 degrees and spray a 9x13-inch pan with cooking spray.
In a large bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, nutmeg, and ground cloves. Set aside.
In a medium bowl, whisk together oil, brown sugar, granulated sugar, eggs, and vanilla.
Pour wet ingredients into dry ingredients. Stir until combined.
Fold in carrots, pineapple, and pecans. Pour batter into prepared pan.
Bake 40 to 45 minutes. Let cake cool completely.
Using an electric mixer, beat butter and cream cheese until smooth.
Beat in the vanilla.
Beat in powdered sugar 1 cup at a time, adding the 2 tablespoons of cream as needed to thin it.
Spread frosting on cake. Store in refrigerator.