Heat one large pan (use either a skillet or a shallow pot) over medium high heat and place the green beans in it. Add the water and cover the pan. Reduce heat to medium. While the beans steam, turn your attention to the glaze.
Measure out the soy sauce and balsamic vinegar, and place them beside the cooktop. Heat a medium pan. Add the butter on medium high heat. When it is melting, start to whisk it. Keep whisking, nearly constantly, as the butter browns.
When butter turns fragrant with nutty caramel notes, turn off the heat, stand back, and add the soy sauce and vinegar As soon as it is safe to come back closer to the cooktop, whisk the sauce until it is incorporated.
Return your attention to the beans: lift the cover and use tongs to toss the beans. There should still be water at the bottom of the pan. When complete, remove the cover, increase the heat to medium high, and pour the browned butter mixture over the beans (use a rubber spatula to get all of it). Toss the beans and serve immediately.
