Add the boiled carrots, brown sugar, melted butter,salt, and ¾ cup of the water to a small blender and puree the mixture.
In the bowl of a stand mixer, whisk together the flours and yeast, reserving about ½ cup of the bread flour.
Add the carrot mixture to the bowl and mix on low for about 2 minutes.
Using the reserved water and flour, add more of each, alternating each ingredient 1 tablespoon at a time while the mixer is running. The dough should be tacky but not too sticky. I used all of the reserved flour and water.
Adjust the speed to medium low and knead with the dough hook for 6 to 8 minutes. The dough should by smooth and easily pliable.
Form the dough into a ball and place it into a greased bowl, turning to coat. Cover with plastic wrap and let rise until doubled, about an hour.
When the dough is ready, press it into a seven inch by ten inch rectangle. Shape it into a loaf by rolling it into an 8 inch log. Place it, seam side down into 8/½ inch by 4 ½ inch loaf pan. Cover with oiled plastic wrap and let rise until it domes above the rim of the pan, about an hour.
Heat the oven to 375 degrees F. When the bread is ready to bake, lightly draw a picture of a carrot on top of the loaf. Place the loaf in the oven and bake for 35 to 40 minutes. The interior of the loaf should be 190 degrees F.
Turn the loaf out onto a cooling rack and immediately brush the top with the melted butter (optional).
Cool completely before slicing.
