In a large pot over medium heat, melt the butter.
Add onion, celery, and garlic; cook until softened, about 5 minutes.
Whisk in the flour to form a roux and cook for 2 minutes, stirring constantly.
Gradually whisk in the seafood stock until smooth.
Stir in the heavy cream and half-and-half; bring to a gentle simmer.
Add crab meat, shrimp, Old Bay seasoning, and cayenne pepper.
Simmer until shrimp are cooked through, about 5 minutes.
Season with salt and black pepper to taste.
Garnish with fresh parsley and serve hot with lemon wedges.