In a bowl, cover the black-eyed peas with 2 to 3 inches/5 to 7.5 cm of cool water and let stand overnight. Drain.
In a large pot, melt butter over medium heat.
Add the onions, garlic, and jalapeño chile. Cook vegetables for 5 minutes until soft.
Add the celery and carrots.
Cover with the chicken or vegetable stock and add thyme, celery seeds, white pepper, bay leaf, and black-eyed peas. Bring to a boil, reduce heat, and simmer for 20 minutes.
Add the potatoes and cook for an additional 25 minutes, until the potatoes are soft.
Stir in the half-and-half and the smoked pork, if using, and return chowder to a simmer. After adding half-and-half, do not allow the chowder to boil.
Season with salt and pepper.
Serve hot.
