In a small saucepan over high heat, bring wine to a boil. Remove from heat, add morel mushrooms, and let stand until soft, about 20 minutes. Lift morels from liquid, squeezing out any excess, and finely chop. Reserve morels and liquid.
Meanwhile, melt butter in a large frying pan over medium-high heat. Add shallots and garlic and cook, stirring often, until soft, about 3 minutes. Increase heat to high, add cremini mushrooms, and cook, stirring often, until almost all their liquid has evaporated and creminis are beginning to brown, 8 to 10 minutes.
Carefully pour wine into pan, leaving behind any sediment from morels, and boil until reduced by about half, 4 to 5 minutes. Add chopped morels, cream, and thyme, and boil, stirring occasionally, until sauce is slightly thickened, 4 to 5 minutes. Stir in the lemon juice and salt and pepper to taste.
Preheat broiler. Spoon mushroom mixture into 6 small ramekins. Sprinkle with cheese and set on a baking sheet.
Broil 4 to 6 inches from heat just until cheese is melted and starting to brown, 2 to 3 minutes.
Note: Nutritional analysis is per serving.