Cut onion in half, and thinly slice. Cut brussels sprouts in half, and cut each half crosswise into thin slices. Place vegetables in separate plastic bags; seal and chill 8 hours.
Melt butter in a large heavy skillet over medium-high heat; add pecans, and sauté 5 minutes or until toasted. Remove pecans from skillet. Add onion, and cook, stirring often, 15 minutes or until caramel colored. Add pecans and brussels sprouts, and cook about 3 minutes or until heated. Sprinkle with salt and pepper.