Put the onions in a large skillet over medium heat. Cook, stirring constantly, until water evaporates, about 10 minutes, taking care not to burn them. You may need to reduce the heat as the onions dry out. Add spiced butter and simmer on low for about 5 minutes. Add ginger, garlic, tomato paste, and berbere. Simmer for 10 to 15 minutes, adding enough wine to make it a thick sauce.
In a medium skillet brown chicken drumsticks with 2 teaspoons of vegetable oil. Add chicken to the sauce and simmer over very low heat for about 30 minutes, stirring occasionally, until the liquid is reduced and the sauce is very thick, occasionally spooning the sauce over the chicken.
10 minutes before turning off the stove, add hard-boiled eggs.
Serve hot with rice or injera.