In a large saucepan, cover the black-eyed peas with water and bring to a boil. Simmer over moderately low heat until tender, about 40 minutes.
Add a generous pinch of salt and let stand for 5 minutes, then drain well.
Meanwhile, in a large saucepan, melt the butter. Add the onion and cook over moderate heat, stirring occasionally, until softened and just starting to brown, about 10 minutes. Add ginger, garlic, chile, and salt, and cook for another minute.
Add the berbere and turmeric and cook, stirring, until fragrant, about 2 minutes. Add the tomatoes and cook, stirring until softened, about 5 minutes.
Pour in the coconut milk and vegetable broth 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 broth mixture and cook over moderately low heat, stirring, until the peas are lightly coated, about 10 minutes. Garnish with scallions and cilantro. and serve over rice or accompanied with cornbread.