Soak the black eyed peas at least 3 hours before cooking. If you can, soak them overnight. Soak the split peas at least 3 hours before cooking, though you needn't soak if you don't want to.
Rinse the black eyed peas and add to a saucepan. Add about 5 cups of water. Bring to a boil. Lower heat and cook until just tender, about 45 minutes. You want them to be al dente to provide a small bit of crunch.
While the black eyed peas are cooking, rinse and pick over the split peas. When the black eyed peas are done, reserve 4 cups of the pot liquor from the black eyed peas. If there is less than 4 cups, add water to bring to the needed amount.
Chop off the tough leaves from the leeks and chop off the root section. Cut the tender part of the leek in 1 inch thick discs, then slice the disc in half, and then chop. Separate to confirm no dirt is in the chopped leeks.
Saute the leeks in a small amount of olive oil until brown, about 10 minutes. If cooking the split peas in an Instant Pot, cook the leeks on Saute Mode in the IP. If cooking the split peas on the stove top, brown the leeks in the pan that you will cook the peas in.
Add the split peas, the pot liquor and water (or broth) to the pot with the sautéed leeks. If cooking the peas in an Instant Pot, set the IP to high pressure and set the timer for 15 minutes. Do an instant release when the timer goes off. If cooking on the stove, bring to a boil, then lower the heat. Cook until the split peas are at the desired texture. Cooking on the stove can take up to 1 hour if the split peas were not soaked.
Add the black eyed peas to the soup. Add water if you want the soup thinner. Mix well. Heat until at the desire temperature.
Ladle the soup into the bowls. Sprinkle the top of the soup with pistachios and pomegranate seeds, if used. Swirl the top with pomegranate molasses.
Enjoy!