If you have thought ahead, cover the black-eyed peas in water and soak overnight. Discard water and rinse the beans.
In a deep, wide, heavy pan, heat olive oil over medium heat. Add celery, onion and pepper and cook 15 minutes, stirring occasionally. Add garlic and cook 15 minutes more, stirring occasionally. Vegetables will have reduced in size and may begin to brown.
In another pan, cook the sausage over medium-high heat, breaking it up and stirring to allow it to cook through. Drain of any fat and add to vegetables after they have cooked.
If you haven’t soaked beans overnight, rinse them well and pick over them (sometimes they’ll include little bits of dirt or rock, though supermarket beans are pretty reliably clean these days). Add beans to pan with vegetables and sausage. Add chicken broth and seasonings. Bring to a boil and reduce heat to simmer. Simmer uncovered for 50 minutes and taste. If the beans still have a little crunch, cook until they are tender, adding water as need. When fi nished, the beans will have some thin sauce but will not be soupy (though adding more liquid and making it soup is certainly acceptable).
Serve over soft polenta (or grits), fried polenta or rice. Serves 8.
To make fried polenta: Cook grits or cornmeal in water or broth. When cooked, pour them in a shallow pan and allow them to cool. Slice into squares and fry in olive oil, chicken fat or frying medium of choice.