Melt the butter in a large soup pot.  Put the onion in the butter and salt and pepper to taste.  Saute onion until translucent and then add the potatoes, 2 cups of water, and the rosemary.  Bring to a boil. Simmer for 20 minutes, until the potatoes are fork tender.

Remove the pot from the heat and mash the potatoes (don’t drain the water) – I just used a potato masher because I like it to be a bit lumpy but you can certainly use an immersion or regular blender or food processor.  To this potato mixture in the soup pot, add the remaining 2 cups of water and bring to a boil.

Reduce to a simmer  (leave uncovered) for 10-15 minutes until it thickens.  You need to stir this often to keep it from sticking.  I found a non-stick pot to be helpful too.  Meanwhile, heat the oil in a skillet and cook the carrots over medium high heat, a few at a time.

Saute for a few minutes until nice and crispy.  Remove to some paper towels and sprinkle with salt to taste right away.  Serve the soup with a topping of the carrots. For an extra burst of flavour and colour, I added a little dollop of sour cream and a bit of chopped cilantro, parsley, or arugula on top too.  Season with more pepper if desired.