Heat 2 tablespoons olive oil in a skillet over medium-high heat. Add 1 thinly sliced fennel bulb and cook, stirring, until browned, 15 minutes. Cook 1 1/2 pounds halved green beans in boiling salted water until tender, 5 to 6 minutes. Drain and add to the fennel. Stir in 2 tablespoons each butter and water and cook until glazed, 2 minutes. Season with salt and pepper.