Add the onions to a large preheated, oiled pan on medium-high heat and stir until they begin to soften.
Add the green beans, black pepper, and a pinch of salt. Stir as necessary to prevent sticking.
When the green beans are almost ready, stir in the garlic and a couple of teaspoos of balsamic vinegar. The earlier you add the garlic the more mellow its flavor will be; I like to get a solid garlic kick, so chose to add it quite near the end.
The balsamic should cook down a bit as the garlic cooks, leaving you with very little liquid.
Stir in the basil*, then adjust salt and pepper levels to taste and serve immediately. These beans are best eaten warm, but they store and reheat well.