If your black-eyed peas are old, soak them overnight in enough water to cover them by at least 1 inch.
When ready to cook the peas, fill a medium pot with water and bring to a boil. Add drained peas, cover the pot, reduce the heat to low, and simmer until peas are fork-tender, between 45 minutes and 1.5 hours. Cooking time varies drastically and depends on the age of your peas, so check them regularly.
Meanwhile, heat the olive oil in your smallest sauté pan over medium-high heat. Add the turmeric and shallots, and cook for 3-4 minutes, until shallots are soft, fragrant, and browned in spots. Add salt, stir to combine, and remove from the heat.
When peas are soft but still retaining their shape, drain them, transfer them to a bowl, and pour the shallot mixture over the peas, making sure to scrape the sauté pan for all those little bits of turmeric and shallot clinging to the bottom. Stir beans to incorporate, taking care not to smush them too much.
Add soy sauce and pomegranate syrup if using, and toss to combine.
Right before serving, fold in pomegran-ates, fresh herbs, and lime juice. Serve at room temperature or slightly chilled.