In a large soup pan. add the clam juice, potatoes, bay leaf, thyme, salt, pepper, paprika, and cayenne together and stir. The liquid should cover the potatoes. If not, add enough water to cover them.
Bring the pot to a simmer and allow to cook for about 15 minutes, or until potatoes are slightly soft.
In a separate pot, heat the half-and-half JUST until it begins to get frothy. DO NOT allow it to boil as it will curdle.
Put all the seafood into the large pot with the potatoes and stir.
Add in the heated half-and-half and the parsley to the pot as well.
Allow the soup to cook but NOT begin to boil until the fish/seafood has cooked for about 8-10 minutes.
Shut off the heat, and allow the soup to simmer for about 30 minutes.
Heat back up to the desired temperature and serve with some toasted bread or soup crackers.