Prepare an ice-water bath. Bring a saucepan of salted water to a boil. Cook fava beans until tender, 1 to 2 minutes. Drain, and transfer to ice-water bath. Let cool. Drain, and peel beans.
Pulse beans, goat cheese, oil, tarragon, lemon zest and juice, 1/2 teaspoon salt, and 1/4 teaspoon pepper in a food processor until just combined but still chunky, about 6 or 7 times. Stir in water. Add an additional tablespoon water if mixture is too thick. Transfer to a bowl. Refrigerate until ready to serve.
Sprinkle with pepper just before serving. Serve with radishes.