Preheat oven to 350 degrees F (175 degrees C). Grease a 9-inch springform pan with butter.
Whisk banana flour, white sugar, brown sugar, baking soda, xanthan gum, and salt together in a large bowl.
Combine 2 cups grated carrots, oil, buttermilk, eggs, and vanilla extract in a blender; pulse until well blended.
Pour blended carrot mixture over banana flour mixture; mix to form a smooth batter. Fold in remaining 1 cup grated carrots and pecans. Pour batter into the prepared pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 50 minutes. Cool for 30 minutes. Run a knife around the sides to loosen; lift off ring.
