Bring a large pot of water to a boil. If using dried morels, put them in a small bowl, cover with 1 cup boiling water, and let stand 10 minutes. Lift out and pat dry.
Meanwhile, generously salt remaining boiling water. Fill a large bowl with ice and cold water and set near the stove. Add asparagus to boiling water and cook until crisp-tender, about 4 minutes. Remove from water and immediately plunge into ice bath to stop cooking. Repeat process with green onions. Drain asparagus and onions on paper towels, then cut asparagus spears in half.
In a large frying pan over medium-low heat, melt butter. Add morels, asparagus, and onions and cook 1 minute, tossing gently to coat with butter. Stir in crème fraîche and season with salt and pepper. Continue cooking until heated through, 4 minutes longer. Transfer to a serving dish.
Note: Nutritional analysis is per serving.