This carrot cake is nothing like its traditional cousin. More like a bread than a cake, it is very moist, very dense, and sugar free! Sweetened only with ripe bananas, dried figs, and prunes, it makes a lovely afternoon snack or could even make a satisfying breakfast. The bananas lend a unique flavor not typically found in a carrot cake, and the pecans add the perfect amount of crunch. 
The frosting is made with Greek yogurt and a little maple syrup. The recipe called for cream cheese, but I'm glad I abstained. The cake turned out so moist and dense that I think cream cheese might be overwhelming. But if you try it with cream cheese, let me know how it goes!
The only changes I plan to make next time: reduce the amount of maple syrup in the frosting (I love my tart Greek yogurt just the way it is) and replace some of the butter with light olive oil. I've got nothing against butter, but something about it lingered in the back of my palate for a looong time, and it felt almost too rich. Almost.
All in all, this cake/bread is fabulously healthy and delicious. Please give it a try!
Inspired by Heidi Swanson at 101 Cookbooks.
2 cups flour (I used 1 cup whole-grain and 1 cup all-purpose)
2 1/2 tsp. baking powder
1 1/2 tsp. cinnamon
3/4 tsp. fine grain sea salt
3/4 cup finely chopped pecans
1 stick unsalted butter, melted
1/2 cup prunes, dried figs, and/or dates, finely chopped into a paste (I used a mini food processor)
3 ripe bananas, mashed well
3 medium carrots, grated
1/2 cup plain Greek yogurt
2 eggs, lightly whisked
6 ounces Greek yogurt or cream cheese
3 Tbsp maple syrup or honey
Preheat the oven to 350. Spray a 9-inch cake pan and line with parchment paper.
Sift the flour, baking powder, cinnamon, and salt. Stir in pecans and set aside.
Stir the dried fruit into the melted butter and set aside.
In a separate bowl, combine the bananas and carrots. Stir in the fruit-butter mixture, breaking up any fruit clumps as you go. Whisk in the yogurt and eggs. Add flour mixture and stir until everything just comes together. Pour into prepared pan.
Bake for 50 minutes, until a toothpick inserted into center comes out clean. Remove from the oven and let cool.
To make frosting, whip or whisk together the Greek yogurt and maple syrup. Spread onto the cake once it has completely cooled.