Whisk together vinegar, water, mustard, shallot, salt, and pepper in a small bowl, then add oil in a slow stream, whisking.
Preheat oven to 400°F.
Melt butter in a large shallow baking pan (1 inch deep) in lower third of oven, about 3 minutes. Toss sprouts in pan with butter, pecans, and salt. Arrange sprouts, cut sides down, in 1 layer and roast in lower third of oven until undersides of sprouts are golden and nuts are fragrant, 12 to 15 minutes.
Whisk vinaigrette, then transfer warm sprouts and nuts to a large bowl and toss with frisée, endive, and enough vinaigrette to coat.
Serve immediately.
Vinaigrette can be made 2 hours ahead and kept at room temperature.Brussels sprouts and nuts can be roasted 2 hours ahead and kept at room temperature. Reheat in a 400F oven until hot, about 5 minutes.