Heat butter in a large pot over medium heat. Add onion and cook 5 minutes. Sprinkle with curry, salt and pepper. Cook 1 minute.
Stir sweet potatoes, carrots and broth into pot. Cover and bring to a boil. Reduce heat and simmer 15 minutes, until potatoes are soft.
Meanwhile, make Onions. Toss sliced onion, flour and curry together in a medium bowl. Heat oil in a medium-size deep saucepan over medium-high heat. Test oil by dropping one onion into hot oil. It should turn light brown in about 3 minutes. Reduce heat if browning too quickly. Add half of the onions to the oil. Cook 4 minutes, turning, until golden. Transfer to paper towel-lined plate. Repeat with remaining onions.
Once soup is done simmering, transfer in batches to a blender or use an immersion blender in pot. Puree until smooth. Stir in brown sugar and serve soup topped with some of the onions.