How to Make It
Rinse the black-eyed peas and chickpeas. Pour them into separate medium saucepans and cover with several inches of water. Cover and cook over moderate heat until tender, about 20 minutes for the black-eyed peas and 1 hour for the chickpeas. Drain the black-eyed peas and discard the liquid. Drain the chickpeas; reserve 1/3 cup of the cooking liquid.
Meanwhile, in a medium saucepan, combine the lentils with 4 cups of water, cover partially and cook over moderate heat until tender, about 40 minutes. Drain; reserve 2 cups of the cooking liquid.
In a large, enameled cast-iron casserole, heat 2 tablespoons of the oil. Add the lamb and cook over moderate heat, stirring occasionally, until browned, about 5 minutes. Stir in the onion, cover and cook until softened but not browned, about 2 minutes. Add the tomato paste, red pepper paste and 1/2 cup of water and bring to a simmer. Cover and cook, stirring once or twice, until the mixture begins to caramelize, about 20 minutes.
Add the purslane, bulgur and the reserved chickpea and lentil cooking liquids to the casserole. Cover and cook for 10 minutes. Add the chickpeas, black-eyed peas, lentils, garlic and enough water to barely cover. Cover and simmer for 5 minutes. Remove from the heat, stir in the lemon juice and season with salt.
In a small skillet, heat the remaining 2 tablespoons of oil. Add the spearmint, Turkish red pepper flakes and 1/4 teaspoon ground black pepper. When the oil begins to sizzle, give it a stir and drizzle it over the stew. Stir once and let stand for 30 minutes. Serve the stew at room temperature or let cool, then refrigerate and serve chilled the following day. Pass the scallions and lemon at the table.