Remove the skin from the chicken legs and split each leg at the joint into drumsticks and thighs. Rinse well and then place in a bowl of cold water with the lime to soak.
In a small bowl, make a thick paste by blending the berbere with about 2 1/2 tablespoons of water. Set aside to allow the spices to mellow slightly.
In a heavy-bottomed sauté pan, cook the onion over medium-low heat, stirring very frequently, for about 15 minutes until soft and translucent. Stir in the oil and 2 tablespoons of the niter kebbeh, add the garlic and ginger, and cook for about 1 minute until aromatic. Stir in the reserved berbere paste, the nigella, cardamom, and ajowan, and season with salt. Add a couple of spoonfuls of water and cook over a low heat for 10 minutes, stirring frequently, to let the aromas smooth out. Add a touch more water if needed to keep the mixture from scorching.
Drain the chicken and gently squeeze to remove any moisture. With a sharp knife, mark the pieces on each side with a pair of diagonal shallow slits. Add the chicken to the pan, coating in the sauce, and cook for about 5 minutes until browned. Add 1 cup (250 ml) of hot water, cover the pot, and simmer for about 15 minutes until the chicken is almost tender. Transfer the chicken to a plate and cover.
Cover the pan with a lid and simmer the sauce over low heat for 1 hour. Add the mekelesha spice blend and cook for a further 15 minutes. Add more water if needed to keep the consistency moist. Return the chicken to the pan to reheat. Make shallow slits horizontally on the boiled eggs and add to the stew. Serve with injera.