Heat 1 tablespoon of the olive oil over medium-low heat in a medium pot. Add the salt, onion, carrot, and garlic and saute for 2-3 minutes. Reduce the heat to low, cover the pot, and let the aromatics soften, but not brown, for about 5 minutes. Take the garbanzo beans and reserve about 1/2 cup from the soup and set them aside. Add the remaining garbanzo beans, 3 cups of chicken stock, and salt pork to the pot. Bring the soup to a boil over high heat and then reduce the heat to low, cover the pot, and let the soup cook for 30 minutes.
Take the pot off the heat, remove the salt pork from the pot and discard. In two batches, puree the soup in the blender until completely smooth. Return the soup to the pot. Add chicken stock if needed to thin the soup and add salt and pepper to taste.
While the soup is cooking, crisp up the prosciutto and leeks. For the prosciutto, start with a dry skillet and heat over medium high until very hot. (Don't use non stick.) Add the prosciutto and cook, stirring constantly, until it's very crisp and browned. Transfer the prosciutto to a plate. In the same skillet, heat the remaining 2 tablespoons of olive oil over medium high heat. Add the leeks and saute until browned and crispy, about 5 minutes. With a slotted spoon, transfer the leeks to a towel lined plate.
To serve the soup, ladle portions into soup bowls. Top with reserved garbanzo beans, crispy leeks and prosciutto, and drizzle with some paprika oil and parsley oil.