In a large saucepan, cook the leek in the butter over moderate heat for 3 minutes, or until softened. Add the broth, peas and seasonings and simmer, covered, for 25 minutes, or until the peas are very tender. In a food processor, blend the mixture in batches until combined well. Let it cool. Chill the soup, covered, for at least 2 hours. Before serving, stir in cream and fresh mint. Garnish with mint sprigs. Correct the seasoning.