Heat 2 tablespoons olive oil in large, heavy kettle over moderate heat 1 minute. Add mushrooms and cook, stirring often, until juices are released and these evaporate, about 5 minutes. Scoop mushrooms to large plate and reserve.
Add remaining 1 tablespoon oil to kettle; also add scallions, onion, garlic and rosemary. Cook and stir until scallions and onion are golden, about 3 minutes. Add corn, broth, salt and pepper; adjust heat so mixture bubbles gently, cover, and simmer 25 minutes.
With slotted spoon, scoop 2 cups soup solids into food processor and Purée until smooth. Return to soup, add shrimp, and simmer just until they turn pink, 2 to 3 minutes.
Mix in cream and reserved mushrooms and bring to a simmer. Taste for salt and pepper, fine-tune, and serve.
Makes: 4 to 6