Preheat oven to 350 degrees. Remove stems from shiitake mushrooms. In a saucepan over medium-low heat, cook cream and spinach until reduced by half. Stir in shallots and cook 1 minute. Remove from heat and stir in coconut milk, cracker crumbs, shrimp, salt, pepper and dill.
Stuff mushroom caps with crab-shrimp mixture.
Place caps in a shallow baking pan. Bake 8 to 10 minutes. Sprinkle tops with Parmesan cheese. In a saucepan, heat oil and 1 tablespoon butter. Cook over gentle heat 20 minutes or until only 1 tablespoon of liquid remains.