Place carrots in a small saucepan; cover with water. Bring to a boil. Reduce heat; cover and simmer for 8-10 minutes or until tender. Drain and cool slightly. Place carrots in a blender or food processor; cover and process until pureed. Add egg and 1/4 cup warm water; process until blended.
In a large bowl, dissolve yeast in remaining water. Add carrot mixture, oil, sugar, molasses, salt and 2-1/2 cups flour; mix well. Stir in enough remaining flour to form a soft dough. Turn onto a floured surface; knead until smooth and elastic, about 6-8 minutes. Place in a greased bowl, turning once to grease top. Cover and let rise in a warm place until doubled, about 1 hour.
Punch dough down. Turn onto a lightly floured surface; divide into 45 pieces. Shape each into a ball; place three balls in each greased muffin cup. Cover and let rise until doubled, about 30 minutes. Bake at 350° for 18-20 minutes or until lightly browned. Brush with butter. Remove from pans to wire racks.