1/4 cup plain yogurt (NOTE: Do not opt for nonfat or Greek.)
1/2 cup Neufchâtel or plain cream cheese, room temperature
1/4 cup raw honey
1 tsp orange zest
Preheat oven to 325˚F. Mist a 9-inch round, nonstick baking pan with cooking spray. Cut out a 9-inch round piece of parchment paper and fit inside pan. Using a food processor fitted with a grating disk, grate carrots. Measure out 1½ cups, lightly packed, and reserve any leftovers for future use. Fit food processor with the metal S-shaped blade and add 1 1/2 cups grated carrots. Pulse until finely chopped, 7 to 9 pulses; set aside.
In a large bowl, whisk together flour, baking powder, cinnamon, ginger, baking soda, salt and cardamom (if using). Set aside.
In the bowl of an electric stand mixer, lightly whisk eggs by hand. Fit mixer with the paddle attachment and add maple sugar, oil and yogurt. Beat on medium speed until light and frothy, about 3 minutes. (NOTE: This step can also be done with a handheld electric mixer.) Add flour mixture in 3 additions and beat on lowest speed, until just incorporated. With a spatula or large spoon, stir in carrots by hand.
Transfer to prepared pan and bake in center of oven until edges are golden brown and a toothpick comes out clean, 35 to 37 minutes. Cool in pan on a wire rack for 10 minutes. Invert cake onto a plate and gently peel off parchment. Invert cake back onto wire rack so cake is right side up. Cool completely.
In the bowl of an electric mixer fitted with the paddle attachment or with an electric handheld mixer, add cream cheese, honey and orange zest. Beat on medium-high until light and smooth, about 2 minutes. Spread over top of cake, leaving a 1/2-inch border around edges.