Place the black-eyed peas in a bowl or pan and cover them with water. Leave them to soak for 8 hours.
Drain the black-eyed peas. Place them in a pan and add 6 cups of water. Bring to a boil and skim off the froth that rises to the top. Reduce heat to medium, cover, and cook the beans 15 minutes. Add the carrots, a quarter of the leek, celery, bay leaves, and 1 1/2 teaspoons salt. Cover and cook the beans 30 minutes.
While black-eyed peas are cooking, heat the oil in a skillet over medium heat. Sauté the onions until they are very soft but not browned, 6 to 8 minutes. If they start to brown, add a few drops of water and continue frying. Slice the remaining leek, add it to the skillet and continue frying.
Place the coarse salt in a mortar with the peppercorns, cloves, coriander, cumin and oregano. Crush the spices and herbs to a powder. Add the garlic and continue crushing to make a paste. Remove the carrots from the pan of black-eyed peas. Cut one carrot in half. Add one half to the mortar mixture and mash it with the spices. (Reserve the remaining carrots.) Dilute the paste with a spoonful of the black-eyed peas cooking liquid.
Stir the paste from the mortar into the sautéed onions in the skillet and fry for 2 minutes more. Stir the contents of the pan into the black-eyed peas. Add the chard and ½ cup of cold water. Continue cooking the beans until they are very tender, about 20 minutes.
Remove and discard the bay leaves, whole piece of leek, and celery. Slice the reserved cooked carrots and return them to the pan. Stir in the lemon juice. Allow the black-eyed peas to sit 10 minutes before serving.
Serve the black-eyed peas in bowls with their liquid or, to serve as a vegetable side dish, remove them from the pan with a slotted spoon. Drizzle olive oil over the top. Garnish with pomegranate arils, if desired.