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Rinse the black-eyed peas in a colander. Place in a pot with ample water and bring to a boil over high heat. Remove from heat, drain and place back in a pot with fresh water. (The reason for this step is to keep the black-eyed peas from turning gray when cooking.)
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Bring back to a boil, cover, and reduce heat to medium-low. Simmer for 35 – 40 minutes or until the black-eyed peas are tender and most of the water absorbed.
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In the meantime, prepare the vegetables: In a large, deep skillet heat 1/3 cup of olive oil and sauté the onion and garlic over medium heat, stirring, until wilted, about 8 minutes. Add the greens and sauté until wilted.
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About halfway through cooking the black-eyed peas, add the sautéed vegetables to the pot. Stir in the vinegar, tomato paste and tomatoes. Season with salt and pepper and continue cooking until done.
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Just before removing from heat, add olives, oregano and remaining olive oil. Serve warm or at room temperature.