Heat 2 tablespoons oil in heavy large pot over medium heat. Add onion, carrot, garlic, and thyme; sauté until vegetables are tender, stirring occasionally, about 10 minutes. Add 4 cups stock and wine; bring to boil. Add mussels; cover and cook until mussels open, about 5 minutes (discard any mussels that do not open). Using slotted spoon, transfer mussels to large bowl; cool slightly. Remove mussels from shells; cover and refrigerate until ready to use. Strain stock mixture and any accumulated mussel liquid into medium bowl; discard vegetables.
Heat remaining 3 tablespoons oil in heavy large skillet over medium heat. Add zucchini; sauté until tender but not brown, about 20 minutes. Add 2 1/2 cups strained stock. Bring to boil. Cool slightly. Puree zucchini soup in batches in blender until smooth. Transfer to large saucepan; mix in cream. Thin with more strained stock, if desired. Reserve any remaining stock for another use. Season with salt and pepper. Refrigerate until cold, about 4 hours. (Soup and mussels can be made 6 hours ahead. Cover separately; keep chilled.)
Divide zucchini soup among 6 bowls. Top each with mussels, dividing equally. Sprinkle with mint.
