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Heat oil in heavy large saucepan over medium-high heat. Add shallots and sauté until golden and almost tender, about 7 minutes. Add peas, 4 cups broth, and 2 tablespoons tarragon; bring to boil. Reduce heat to medium and boil until flavors blend and peas are tender, about 7 minutes. Cool slightly.
Working in batches, puree soup in blender until completely smooth. Return soup to same saucepan. Bring to simmer and thin with more broth by ¼ cupfuls, if desired. Stir in remaining 1 tablespoon tarragon. Season with pepper.
Ladle soup into 6 bowls. Drizzle lightly with yogurt.