Place sliced leeks in a large bowl of cold water and let stand for 5 minutes to rid them of dirt and sand. Lift out of the water and drain in a colander. Set aside.
In a small stockpot, heat oil over low heat. Add leeks and cook until wilted, about 10 minutes. Add peppers, tarragon, stock, and salt and pepper to taste. Raise heat to high; bring to a boil. Lower heat and simmer until peppers are very tender, about 20 minutes.
Remove from heat and discard tarragon sprigs. Transfer soup to a food processor and puree. Pass puree through a fine strainer and adjust seasoning with salt and pepper, if necessary. Divide soup among 4 bowls and place 2 of the toast pieces in each. Garnish with tarragon leaves and drizzle with olive oil, if desired. Serve immediately.