Bring a large stockpot of salted water to a boil. Add the green beans and cook until bright green, approximately 1 minute. Remove the green beans from the pot and place them into an ice bath.
Heat the oil and 1 tablespoon of the butter in a large saute pan over medium heat. Add the shallots and garlic and cook, stirring to mix well until the shallots are softened, 3 to 4 minutes. Add the potatoes and remaining tablespoon of butter and sprinkle with salt and pepper. Cook the potatoes, stirring occasionally, until just tender, about 10 minutes. Add the green beans to the pan and cook until they are heated through, 3 to 4 minutes more. Season with salt and pepper.