PREHEAT the oven to 400 F. Line a baking sheet with parchment paper.
BRING the balsamic vinegar to a boil in a small saucepan over medium-high heat. Turn the heat down to low and simmer until the balsamic is reduced by about half. 20 to 30 minutes. Remove from the heat, allow to cool and reserve.
WHILE the glaze is reducing, combine the sweet potato and a bit of the cooking fat in a bowl and toss to coat evenly. Spread the coated sweet potatoes evenly on the prepared baking sheet.
MEANWHILE, coat a large skillet in cooking spray over medium-high heat. When the skillet is hot add the Brussels sprouts and cook, shaking the pan occasionally as they start to brown, for 3 to 4 minutes. Add the onion and garlic and continue to cook, stirring, until the garlic is aromatic, an additional minute. Season with salt and pepper.
ADD the Brussels sprout mixture to the sweet potatoes on the pan, spreading them evenly without crowding. Put the baking sheet in the oven and roast for 15 to 18 minutes, until the sweet potatoes are golden brown and soft and the sprouts are tender.
PLATE the Brussels sprouts and sweet potato mixture and drizzle with the balsamic glaze.