Pick through several cups of dried peas to remove debris. Soak overnight (or at least four hours) in ample, room temperature water.
Drain, rinse and return to a large pot. Cover with water by a few inches, add the large pieces of celery, peeled carrot and/or a bay leaf and bring to a boil.
Boil for 15 minutes, scooping off the white foam from the surface as best you can. Cover and reduce to a simmer. Test the beans for doneness after 20 minutes (they may take up to 45 minutes depending on the age of the beans). You want tender, but not mushy, beans. Add sea salt during the last 5 minutes of cooking. Drain the beans and return them to the pot to cool. Remove the celery, carrot and bay leaf before serving.