Place the brown sugar, egg and canola oil in an electric mixing bowl. Mix this for three minutes. Add the sourdough discard and the milk. Mix until incorporated.
Add the dry ingredients. Mix the ingredients together using a spatula. Add the shredded carrots. Make sure to mix and dig into the bottom of the bowl to incorporate the dry ingredients with the wet.
Transfer to the prepared pan. Level the batter and bake for eighteen to twenty minutes in the preheated 350 F oven , or until the toothpick comes out clean.