Melt butter in a medium saucepan over medium heat. Add onion, and cook until softened, about 4 minutes. Add carrots, and cook for 2 minutes, stirring occasionally. Add water, and bring to a boil. Reduce heat, and simmer until carrots are very soft, 25 to 30 minutes.
Filling a blender halfway and covering with a kitchen towel, puree soup in batches. Stir in honey, and season with saltand pepper. Chill soup for at least 3 hours or up to overnight.
Before serving, prepare breadcrumbs: Heat olive oil in a medium-size saute pan over medium-high heat. Add fresh unseasoned coarse breadcrumbs. Stir constantly until toasted and golden brown, about 2 minutes. Transfer to a bowl, and let cool. Stir in finely chopped fresh flat-leaf parsley, and season with salt and pepper. Garnish each serving with 1 tablespoon breadcrumb mixture, and thinly sliced baby carrots if desired.