1Preheat oven to 350 degrees F (175 degrees C). Grease two 4x8-inch loaf pans.
2Combine flour, baking soda, baking powder, cinnamon, and salt together in a bowl. Beat brown sugar and butter together in a separate bowl using an electric mixer until smooth and creamy. Stir flour mixture, alternating with bananas, into creamed butter mixture just until batter is mixed; fold in carrots and walnuts. Pour into the prepared loaf pans.
3Bake in the preheated oven until a toothpick inserted in the center of a loaf comes out clean, 50 to 60 minutes.