How to Make It
In a bowl, rub the chicken with the lime juice, 1 teaspoon of the thyme, 1 tablespoon of the berbere and a generous pinch each of salt and pepper. Let stand for 30 minutes.
Preheat the oven to 350°. In a large, deep ovenproof skillet, melt the butter. Add the onions and cook over moderately low heat, stirring, until golden and softened, about 25 minutes. Stir in the garlic, habanero, ginger and the remaining thyme and cook until fragrant, 1 minute. Add the tomato paste and the remaining berbere. Cook over moderate heat until glossy, about 5 minutes. Add the wine and cook until almost evaporated, 3 minutes. Stir in the stock; bring to a boil. Add the chicken, cover and bake for 40 minutes, until tender; turn halfway through baking.
Shred the chicken with 2 forks. Simmer over moderately high heat until the sauce has thickened, 5 minutes. Stir in half the eggs and season with salt and pepper. Serve with tortillas and the remaining eggs.