In a 4 or 5 qt Dutch oven, melt butter over med heat. Add onion, salt, and pepper. Cook, stirring occasionally, until onions are translucent but not brown. Add potatoes, 2 cups water, and rosemary. Bring to boiling, reduce heat and simmer, covered, until potatoes are fork-tender (abt 20 mins). Remove from heat.
With potato masher, mash potatoes until no lumps remain. Return to Dutch oven. Add remaining 2 cups water and bring to a boil. Reduce heat and simmer abt 10 mins, until thickened and desired consistency, stirring often to prevent sticking.
While soup is simmering, in a 10" skillet melt oil over med-high heat. Add carrot ribbons, a few at a time, to hot oil. Cook for 1-2 mins or until crisp. Transfer to cooling rack or paper towels, immediately sprinkle with salt.
Spoon soup into serving bowls; top with crispy carrots and sprinkle with coarse-ground black pepper.