Preheat oven to 450F/220C. Spray an extra-large baking sheet with olive oil or non-stick spray.
Peel sweet potatoes and cut into chunks about 1 inch across. Put the sweet potatoes into a bowl and toss with 1 tablespoon olive oil, 1.5 teaspoons balsamic vinegar, salt, and pepper.
Spread sweet potatoes out on the baking sheet and roast for 20 minutes.
While the sweet potatoes are roasting, wash the brussels sprouts and spin dry or pat dry with paper towels. Trim the ends, then cut the brussels sprouts in half lengthwise. (Discard any leaves that fall off; they tend to burn in the hot oven.)
Toss the cut brussels sprouts with the other tablespoon of olive oil, the other 1.5 teaspoons of balsamic vinegar, and a little salt and pepper.
When sweet potatoes have cooked for 20 minutes, remove the baking sheet and toss sweet potatoes with the brussels sprouts.
Roast 20 minutes more, or until the sweet potatoes are cooked through and both vegetables are slightly browned. (If your oven runs hot, I would check them after 15 minutes.)
Serve hot, sprinkled with the Parmesan (or Feta) as desired.
Roasted Brussels Sprouts and Sweet Potatoes with Balsamic Vinegar https://gourmetliving.org/brussels-sprouts-and-sweet-potatoes-with-balsamic/