Preheat oven to 375°F and line a baking sheet with parchment paper. Poke sweet potatoes with fork and place on prepared baking sheet. Bake, flipping after 30 minutes, until very tender and beginning to pop, about 60-75 minutes. Cut in half lengthwise when fully cooked.
Thinly slice enough light green parts of leeks to make 1 packed cup and set aside. Roughly chop remaining leeks.
Heat 2 Tbsp oil over medium-low heat in a large soup pot or Dutch oven. Add chopped leeks, 2 tsp salt and 1 tsp pepper. Cook, stirring occasionally, about 10 minutes. Add broth and simmer until leeks are very tender, about 6-8 minutes.
When cool enough to handle, remove sweet potato flesh from the skin. Add flesh to pot and return to a simmer; stir in nutmeg.
Puree in blender or food processer with ghee (if using) until smooth. Taste and add additional salt and pepper to taste, if needed.
Meanwhile, heat remaining oil in medium skillet over medium heat. Add sliced leeks and a pinch of salt; saute until tender, about 2 minutes.
To serve, add a dollop of yogurt or swirl it into soup (combined with 1 Tbsp water to thin) and garnish with sauteed leeks and pecans.