Heat the oven to 425°F. Toss cremini and shiitake caps with olive oil, 1/2 teaspoon salt and pepper on a large rimmed sheet. Roast for 25 to 30 minutes, turning once, until browned and the released moisture has mostly evaporated.
Melt butter in a soup pot over medium heat. Cook shallots for 5 minutes and garlic for 30 seconds, then add sherry and simmer for 2 minutes.
Scrape roasted mushrooms and their juices into the pot. Add broth, thyme and remaining salt and simmer for 10 minutes.
Transfer half the soup, including mushrooms, to a heat-safe blending container and puree carefully. Return to the pot, leaving the other mushrooms in pieces.
Stir in crème fraîche over low heat until melted and steaming, about 3 minutes. Divide among 4 bowls without boiling the finished soup hard.