Preheat oven to 375°F Line a 13x9-inch metal baking pan with foil, leaving a 2-inch overhang at each end. Lightly butter foil.
In a bowl, combine bran cereal, carrots, milk, pineapple and yogurt; let stand for 5 minutes. In a large bowl, combine flour, baking powder, cinnamon, baking soda and salt. Whisk egg and honey into milk mixture. Pour over dry ingredients and stir just until mostened.
Spread into prepared pan, smoothing top. Bake for about 30 minutes or until a tester inserted in center comes out clean. Let cool completely in pan on rack. Using foil overhang as handles, remove from pan and cut into bars.