Whole wheat flour, oat bran, and shredded zucchini and carrots give a boost of fiber to this wholesome bread. Choose small zucchini, which will be younger and more tender for baking. Shred the zucchini onto paper towels to absorb some of the excess moisture.
Lightly coat the inside of a 4-quart slow cooker with cooking spray. In a large bowl stir together all-purpose flour, whole wheat flour, oat bran, baking powder, salt, and cinnamon. Stir in zucchini, carrots, and walnuts.
In a medium bowl whisk together granulated sugar, brown sugar, milk, butter, eggs, and vanilla until sugar dissolves. Add sugar mixture all at once to flour mixture. Stir just until moistened. Spoon into prepared slow cooker.
Cover and cook on high-heat setting for 1-1/2 to 2 hours. Turn off cooker. Carefully remove lid so condensation from lid does not drip onto bread. Cover opening of slow cooker completely with paper towels; place lid on top. Cool for 10 to 15 minutes. Run a knife around edges of slow cooker; remove bread from cooker. Cool completely on a wire rack.