Bring a large pot of water to a boil. Add the green beans and cook for 3 minutes, until bright green and crisp-tender. Drain in a colander and rinse with cold water. Set aside.
In a large, high-sided skillet or Dutch oven, melt 2 tablespoons of butter over medium heat. Add the shallots. Cook, stirring occasionally, until soft–about 3 minutes. Add the green beans and remaining 1 tablespoon of butter. Cook, tossing occasionally, for about 5 minutes. Season to taste with salt and pepper. Transfer to a serving dish and top with walnuts and goat cheese. Serve warm.