Heat the oil in a large skillet over medium-high heat and add the carrots, celery and onion. Season with salt and pepper to taste and cook for about 3-5 minutes, stirring often until tender. Add the black-eyed peas to the skillet along with 2 cups of water. Bring to a boil.
Place your ham in a slow-cooker and pour the black-eyed pea mixture over it, mix it all up well. Cook on LOW for 4-6 hours. You may season the pot with some additional salt & pepper to taste! Serve over rice with some hot sauce. Great sides are cornbread and turnip greens!