Step 1

Preheat oven to 350°F. Spray a tube or Bundt cake pan with a generous amount of baking spray. Combine carrots, candied apricots, orange peels, and pistachios in a large bowl. Combine oil, brown sugar, eggs, and orange zest and juice in a high-speed blender or the bowl of a food processor. Pulse on high speed until mixture is emulsified (about 10 pulses). Fold oil mixture into carrot mixture in bowl.

Step 2

In a separate large bowl, whisk together flour, baking powder, cardamom, ginger, baking soda, and salt. Make a well in center of flour mixture; add carrot mixture, and fold to incorporate until there are no visible flecks of flour left behind. Spoon mixture into prepared pan; shake pan lightly to even out the batter and release any air bubbles.

Step 3

Bake in preheated oven 55 minutes to 1 hour, rotating pan on rack halfway through baking time. (The cake is done when a skewer comes out clean when inserted in center of cake and top of cake is firm to the touch and golden brown.) Let cake cool in pan on a wire rack 10 minutes. Invert cake onto wire rack. Let cake cool completely.

Step 4

In the bowl of a stand mixer fitted with the whisk attachment, beat cream cheese and butter on medium speed until mixture is light and fluffy, 4 to 5 minutes. Scrape down sides of bowl, and add 3/4 cup powdered sugar. Beat on low speed until mixture is smooth, about 1 minute. Add sour cream and orange zest and juice, and beat on low speed 1 minute. Add remaining 3/4 cup powdered sugar, and beat on low speed until sugar is completely incorporated, about 45 seconds. Scrape sides of bowl, and increase speed to medium-high; whisk until mixture is well combined. Drizzle glaze on cooled cake; garnish with orange zest.