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