1. Melt the butter in a large deep skillet. Add the onions and 3 tablespoons of the vinegar and cook over moderate heat until they begin to brown, 5 to 6 minutes.
2. Meanwhile, steam the brussels sprouts until crisp-tender, 4 to 5 minutes. Add the brussels sprouts to the onions. Stir in the sugar and the remaining 3 tablespoons of vinegar and cook over moderately high heat, tossing, until the brussels sprouts are tender and lightly caramelized, 8 to 10 minutes. Season with salt and pepper. Transfer to a bowl, garnish with the pistachios and serve.