1. In a 4- to 5-quart pan, bring 3 quarts of lightly salted water to a boil over high heat. Drop in the string beans a handful at a time and bring back to a boil. Lower the heat and cook uncovered for 8 to 10 minutes, or until the beans are tender but still slightly resistant to the bite. Drain the beans, wash them under cold running water and set aside.
2. Melt the butter in a heavy 10- to 12-inch skillet or 2-quart casserole set over high heat. Add the onions and green pepper, lower the heat and, stirring occasionally, cook 5 to 8 minutes, or until the vegetables are tender but not brown.
3. Stir in the tomatoes and basil, raise the heat to high, and boil rapidly for 1 or 2 minutes, until most of the juices in the pan have evaporated. Stir in the green beans and simmer 1or 2 minutes until heated through.
4. In a mixing bowl, beat together the egg, sour cream, salt and a few grindings of black pepper. Taste for seasoning and stir into the vegetables. Transfer to a serving bowl and serve at once.