If using fresh meat, pound, slice, and mince it. If you are using canned abalone, drain off the juice, chop the meat, and instead add it when you add the potatoes.
Melt the butter in a saucepan. Sauté the onion, bell peppers, parsley, and celery for 5 or 6 minutes. Stir in the flour and cook, stirring as you go, until the mixture thickens a little.
Add the abalone, chicken stock, salt, freshly ground black pepper, and perhaps a little cayenne. Bring to a boil, reduce the heat, cover tightly, and simmer for an hour.
Add the potatoes and cook for 12 to 15 minutes, until the potatoes are soft.
Stir in the cream shortly before serving. Serve hot in bowls.