Bring a large pot of salted water to a boil. Fill a large bowl with ice water; generously salt the water.
Add the green beans to the boiling water and cook until bright green and just tender, 4 to 6 minutes. Drain and transfer to the ice water to cool completely. Drain again and transfer to a paper towel–lined baking sheet; pat dry.
Meanwhile, melt 2 tablespoons butter in a large wide pot over medium-high heat. Add the shallots, season with salt and cook, stirring, until slightly softened, 3 to 4 minutes.
Add the green beans to the pot; season with salt and pepper. Cook, stirring, until hot, 4 to 6 minutes. Remove from the heat and add 1 tablespoon water and the remaining 1 tablespoon butter; stir to coat.
You can prep the green beans a day ahead: Follow the recipe through the end of step 2, then wrap the blanched beans in paper towels, place in a resealable plastic bag and refrigerate.