Place the black-eyed peas in a large container, and cover with cold water by 2″. Cover, place in the refrigerator, and let the peas soak for at least 8 hours or overnight.
Drain peas, and transfer to a food processor; pulse until slightly broken and skins break away from peas, about 8 pulses. Transfer peas to a medium bowl, and cover with water; rub peas in water between the palms of your hands to loosen the skins. Let peas sit until skins float to top of water. Slowly drain water from peas, allowing skins to drain with water; add more water if necessary, and repeat rubbing and draining process until all skins are removed from peas.
Place peas in a blender along with baking soda, onion, salt and pepper, and 3 tbsp. water; purée, scraping down sides of blender if necessary, until smooth.
Pour oil to a depth of 2″ in a 6–qt. Dutch oven, and heat over medium-high heat until a deep-fry thermometer reads 365°. Working in batches, use two small spoons to drop tablespoon-sized balls of batter in oil, and cook until golden brown, about 3 minutes.
Transfer fritters to paper towels to drain, and sprinkle with salt. Serve with kaani sauce (see below).