In a small bowl, mix together spices (cinnamon through nutmeg). Reserve 2 teaspoons of this chai spice mix for the frosting. In a medium bowl, thoroughly whisk together flour, baking powder, baking soda, salt, and the bowl of chai spice mix.
Preheat oven to 350 F. In a large bowl with an electric mixer, blend together carrots, granulated sugar, brown sugar, vegetable oil, and eggs. With a spatula, fold dry ingredients into carrot mixture until just combined. Pour into a greased 9x13-inch baking dish. Bake 40 to 45 minutes, or until tester comes out clean. Remove from oven and let cool.
With an electric mixer, blend cream cheese, butter, powdered sugar, milk, and remaining 2 teaspoons chai spice mix. Add milk to desired consistency. Frost cake when both cake and frosting are at room temperature.
Per serving: 388 calories, 18 grams fat (6 grams saturated fat), 50 milligrams cholesterol, 199 milligrams sodium, 54 grams total carbohydrates, 1 gram fiber, 4 grams protein.
