Cook the beans in heavily salted, boiling water until quite tender, about 10 minutes. Drain. Cool rapidly in an ice bath. Drain very thoroughly on a towel.
Purée the beans in a food processor until quite smooth. Add the crème fraîche and continue to process until the cream is fully incorporated.
Just before serving, melt the butter in a saucepan over medium heat. Cook the butter until it starts to brown. Add the purée and stir with a wooden spoon until the purée is heated through. Season with salt and pepper.