Heat olive oil in a skillet over medium heat; cook and stir shredded Brussels sprouts in the hot oil until slightly softened, about 5 minutes. Reduce heat to low; cook and stir pecans into the Brussels sprouts until pecans are fragrant and toasted, about 2 minutes.
Stir orange juice into Brussels sprouts mixture; fold in cranberries and ginger. Simmer mixture until juice is mostly evaporated, about 5 minutes.
