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In a large bowl, combine the black-eyed peas (beans), baking soda, and water to cover by about 2 inches. Cover the bowl with a tea towel and soak peas for at least 8 hours or overnight. Drain, rinse, and drain again.
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In a large saucepan, heat the oil over medium heat. Add the onion, carrots, celery, garlic and a generous pinch of salt and cook, stirring occasionally, until the vegetables begin to soften, 8–10 minutes. Add the cumin, onion powder, sugar, smoked paprika, ginger and cayenne and cook, stirring, until fragrant, 1–2 minutes.
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Stir in the diced tomatoes with their juice and the tomato paste (purée). Bring to a simmer and cook, stirring occasionally, until the mixture thickens slightly, about 5 minutes. Add the drained peas, stock, salt and black pepper. Increase the heat to medium-high and bring the mixture to a simmer, then reduce the heat to medium-low, partially cover, and cook, stirring occasionally, until the peas are tender and creamy, 1 1/2–2 hours. If the pot begins to look dry during cooking, add more stock, 1/2 cup (4 fl. oz.) at a time. Taste and add more salt and pepper, if desired.
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Remove the pan from the heat and let rest for about 10 minutes. Serve hot or warm, drizzled with more oil and sprinkled with chopped cilantro.