Prep Time: 50 minutes
In a large soup pot, heat the olive oil over medium-low flame until hot. Add the leeks and stir continuously until completely tender, about 15 minutes. Add the carrots along with a pinch of salt and pepper and continue to stir for another 3 minutes. Add the sweet potatoes and broth. If necessary, add water until the liquid is covering the potatoes. Top with a lid and continue to cook for 30 minutes, stirring occasionally.
Meanwhile, make crispy shallots by heating the cooking oil in a small pot over a low flame until hot. Add the shallots and fry until light brown, stirring frequently, about 8 minutes. Remove to a plate lined with paper towels using a slotted spoon. Increase the flame under the oil to high. Wait 2 minutes, then fry the shallots a second time until very crispy, about 1-2 minutes. Remove to a plate lined with paper towels and season with a pinch of salt. Set aside.When the potatoes are cooked and easily pierced with a fork, add the cream or milk. Remove from the heat and season with a pinch of salt and pepper. Using a blender or stick blender, puree the soup until smooth. Season to taste. Divide between 4 bowls and top evenly with the shallots.