First, mix the fruit juice, balsamic vinegar, maple syrup, and ginger in a small bowl and set aside. Then heat 1 Tbsp of the butter and the olive oil until the butter is foaming. Add the green beans and salt and stir around. Pat them down until you get as many as possible of the beans in contact with the pan. Cook over med. high heat without stirring until the beans are getting brown (about 5 min). Flip the beans with a spatula and cook some more (3-4 min) until more of the beans are brown. Repeat until you get browning on multiple sides of the beans. (don't stir a lot: more brown = more flavor!) Pour in the chicken broth, slowly. It will sputter, but don't turn down the heat. Cover, cook for another 4-5 min. Most of the liquid will evaporate, and the beans will be tender. Now pour in the pomegranate juice mixture from step one. Cook a couple of minutes more so the sauce gets syrupy. Remove from heat. Finally, add the remaining Tbsp butter (chop it into 4-6 pieces first) and some pine nuts or sliced almonds or pecans (toasting them first makes them more flavorful.) It will make a nice delicious silky glaze.