Cook the green beans in boiling salted water to cover 3 to 4 minutes, or until crisp tender. Drain. Plunge the beans into ice water to stop the cooking process; drain.
Melt the butter and brown sugar with olive oil in a large skillet over medium-high heat; add shallots, and saute 2 minutes. Reduce the heat to medium-low, add vinegar, and saute 10 minutes or until the shallots are golden brown and tender.
Increase the heat to medium-high; add the green beans. Saute 5 minutes or until thoroughly heated. Season with salt and freshly ground black pepper to taste.