Melt the butter in a medium skillet over low heat. Skim foam that rises to the top. When most of it subsides, add the remaining ingredients. Continue cooking, stirring occasionally, for 20 minutes. Strain through a fine-mesh sieve. (Can be made one week ahead and stored in the refrigerator).
Heat a Dutch oven (or a heavy saucepan with a lid) on medium-high heat and add the onions. Let cook undisturbed until they turn dark brown, about 4 minutes. Stir in 2 tablespoons of the Spicy Butter and a teaspoon of salt. Reduce heat to medium-low. Cook, stirring occasionally, until the onions are very tender, 15 minutes. Stir in the remaining 2 tablespoons Spicy Butter (reserve the rest for another use), ginger, and garlic. Cook 1 minute. Stir in the chili powder, cardamom, black pepper, and cloves. Cook for 5 minutes.
Pour in the stock and wine, bring liquid to a simmer and let mixture cook for 10 minutes or so, until the liquid is reduced by about half. Stir in the chicken and cook, stirring occasionally, until the chicken is just done but still tender, 15 to 20 minutes longer. Stir in lime juice and remaining 1 teaspoon salt. Garnish with basil. Serve with eggs, tomatoes, lime wedges, and bread for sopping up the sauce.