In 4- to 6-quart Dutch oven cook mushrooms, celery, onion, and garlic in hot oil over medium heat for 5 minutes or until softened. Add carrots and broth to mixture. Bring to boiling; reduce heat. Simmer, covered, for 20 minutes or until tender.
Let soup cool slightly. Cut up tofu. Place the tofu and half of the broth mixture in a large food processor or blender. (If you don't have a large food processor or blender, process mixture in smaller batches.) Cover and process or blend until smooth. Repeat with remaining broth mixture and evaporated milk. Cover and process or blend until smooth. Return all blended soup to Dutch oven and heat through. Stir in the 1 teaspoon thyme and salt and pepper to taste. Top servings with sour cream thinned with the 2 to 3 teaspoons water and, if desired, additional thyme and cayenne pepper.