In a large skillet, melt 2 tablespoons of butter over medium heat. Add the shrimp and cook for 2-3 minutes per side, until pink and opaque. Remove from heat, chop into bite-sized pieces, and set aside.
If your crab meat is not prepped, gently pick through it to remove any shell fragments. Set aside.
In a large pot, melt the remaining 2 tablespoons of butter over medium heat. Add chopped onion, garlic, carrot, and celery, and sauté for about 5 minutes, until the vegetables are tender.
Sprinkle the flour over the vegetables, stirring constantly for about 2 minutes to form a roux.
Slowly add the white wine to deglaze the pot, stirring continuously. Add the seafood or chicken stock, and bring the mixture to a simmer for about 15 minutes.
Using an immersion blender, blend the bisque until smooth. Alternatively, transfer the mixture to a regular blender in batches, and then return it to the pot.
Stir in the heavy cream and brandy, if using. Bring to a gentle simmer.
Add the cooked shrimp and crab meat, Old Bay seasoning, paprika, salt, and pepper. Simmer for 5 minutes to heat through, making sure the seafood doesn’t overcook.
Taste and adjust the seasoning if necessary. Serve the bisque in bowls, garnished with fresh parsley, lemon wedges, and extra seafood if desired.