There are many versions of this dish, with slight changes in the ingredients and/or their measurements. This version is the one that I settled on, and it has never failed to please. You can serve this over rice, pasta, etc., as it is very rich.
Preheat oven to 375 degrees. Butter an oblong baking dish and set aside.
Melt 4-1/2 T. butter, then blend in flour to make a roux. Slowly add milk and cream, stirring constantly until thick. Stir in sherry and Worcestershire sauce, then add salt and pepper, to taste, and set aside.
In remaining 2 T. butter, saute mushrooms gently for about 5 minutes, until soft. Set aside.
Arrange artichoke hearts in single layer in baking dish. Scatter shrimp on top of artichokes, then cover shrimp with sautéed mushrooms. Pour cream sauce over baking dish, then sprinkle with parmesan cheese and paprika.
Bake 20-30 minutes until bubbly and shrimp is cooked through.