Fresh black-eyed peas cook much more quickly than dried ones do; check for tenderness after 20 minutes.
Place either fresh or dried black-eyed peas in a colander, and rinse them under cool running water. Transfer to a medium stockpot. Cover with about 2 inches of water. Add the peppercorns, bay leaf, onion, jalapeno pepper, ham hock, parsley (including stems), and garlic. Cover, and bring just below the boiling point over medium-high heat. Uncover, reduce heat to a simmer, and cook just until the peas are tender when bitten, about 45 minutes for dried peas (though cooking time will vary with the age of dried peas). Do not stir the peas while they are cooking because they can break down too much. Add salt and pepper to taste during the last 10 minutes of cooking.
The peas will keep in their cooking liquid for about 3 hours at room temperature. Then they may be stored in an airtight container in the refrigerator for 1 to 2 days. Serve black-eyed peas hot, along with their cooking liquid, in individual bowls. If desired, the meat from the ham hock may be shredded and served with the peas, along with the garlic and jalapeno peppers from the pot. Serve with hot skillet cornbread.