Preheat the oven to 350 degrees F.
Liberally rub your bundt pan with softened butter or GF nonstick baking spray. Using your fingers, distribute the fat deep into the nooks and crannies of the bundt cake pan. Once the inside is totally greased, dust evenly with a layer of GF flour. Make sure the grease and flour line every inch of the inside of the pan. If you are careful here, your cake will not stick to the pan after baking. Set the prepared pan aside.
To a large bowl, add the brown sugar, granulated sugar, and vegetable oil. Whisk to combine.
Then add the eggs, applesauce, and vanilla extract to the bowl and whisk until everything is homogenous.
In a separate bowl, add the flour, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg. Whisk to combine.
Using a spatula, fold the dry ingredients into the wet ingredients. When it is almost combined, add the carrots and roasted pecans. Fold until all of the flour is just incorporated.
Evenly pour the cake batter into the prepared bundt pan. Place in a preheated oven and bake 50-55 minutes until a cake tester inserted into the center comes out clean.
Once the cake is baked, remove it from the oven. Allow the cake to cool for 15-30 minutes before turning it out.
Place an inverted plate or cake stand on top of the warm cake pan. Holding the plate tightly, flip the bundt pan so that the cake wiggles out onto the plate. If you greased the pan well, the Carrot Bundt Cake will let loose from the pan. Remove the cake pan to reveal your stunning cake.
Once the cake is cooled, make the icing.
Using a whisk, combine all icing ingredients together until there are no lumps. Warm the icing in the microwave for 30-second intervals until it is a drizzling consistency. Drizzle the icing over the cake.
Serve at room temperature or warm slices in the microwave. Save leftovers in an airtight container in the fridge.