Rinse the black-eyed peas in a colander under cold running water. In a large saucepan, combine the peas with 6 cups of water and bring to a boil. Simmer over moderately low heat until tender, about 40 minutes, stirring occasionally and adding extra water if needed. Add a generous pinch of salt and let stand for 5 minutes, then drain and set aside.
Meanwhile, in another large saucepan or Dutch oven, melt the butter over medium heat. Add the onion, ginger, garlic and chile, and cook, stirring occasionally, about 10 minutes.
Add the berbere and turmeric, and cook, stirring, until fragrant, about 2 minutes. Add the tomatoes and cook, stirring occasionally, until softened, about 5 minutes.
Stir in the coconut milk and stock and bring to a boil. Simmer over moderately low heat, stirring occasionally, until the tomatoes break down and the sauce is thickened, about 20 minutes.
Add the peas to the sauce and cook over moderately low heat, stirring occasionally, about 10 minutes. Stir in the cilantro and scallions, and taste and adjust seasoning with salt, if needed (we found a little salt brought the flavor to life). Serve in soup bowls—you can serve over cooked white rice to feed more guests.