Preheat the oven to 425°F. Line a baking sheet with aluminum foil or a silicone baking sheet.
In a bowl, toss the brussels sprouts with 2 tablespoons of olive oil, garlic powder, salt and pepper.
Arrange the brussels sprouts on the baking sheet then place in the oven for 20 minutes.
Meanwhile, sauté the onions over medium heat in the remaining olive oil for about 10 minutes before adding the pecans. Continue sautéing until the onions are caramelized golden brown.
In a small sauce pan over medium heat, stir together the apple cider vinegar, water, maple syrup and mustard. Allow the sauce to reduce slightly, about five minutes.
Once the brussel sprouts have roasted and are golden brown, remove them from the oven and transfer them to a bowl. Add the onions and pecans and drizzle on the maple mustard sauce. Sprinkle the cheese on top and serve immediately.