Melt the butter in a large saucepan over medium heat until it begins to foam.
Cook and stir the celery, onion, and red bell pepper in the hot butter until soft, about 10 minutes.
Stir the half-and-half and parsley through the vegetable mixture; season with salt and black pepper.
Continue cooking until the mixture just begins to boil; add the oysters and any liquid from the can to the stew along with Louisiana-style hot sauce. Bring the mixture to a simmer and cook until the oysters begin to curl, 10 to 15 minutes more.
Remove the saucepan from heat and allow the stew to sit 5 minutes before serving.