In a large pot, melt the butter over medium heat. Add the chopped onion and cook until soft and translucent, about 5 minutes. Add the minced garlic and sauté for another minute.
Stir in the corn and cook for about 3 minutes, allowing the kernels to soften and release their sweetness.
Add the chicken or seafood stock and bring the mixture to a boil. Reduce heat to low, cover, and simmer for 10 minutes.
Using an immersion blender or transferring the mixture to a blender, puree the soup until smooth, leaving some texture if desired.
Return the soup to the pot and stir in the heavy cream, half-and-half, Old Bay seasoning, cayenne pepper (if using), thyme, and salt and pepper to taste. Simmer for an additional 5 minutes to combine the flavors.
Gently fold in the crabmeat and lemon juice, and cook for 2-3 minutes until the crab is heated through.
Ladle the bisque into bowls, garnish with fresh parsley, and serve with crusty bread on the side.
