Heat oil over med-high heat for one minute. Add garlic and ginger. Cook, stirring, until garlic colors--about 1 minute. Add beans, cayenne and coconut milk. Bring to a boil, then lower heat for simmering.
Cook until most of the coconut milk is absorbed and beans are very soft, about 20 minutes. Stir in lime juice. Taste; use salt and pepper for seasoning if desired.