Simmer sweet potatoes in salted water, peel and cut into cubes. Clean the Brussels sprouts, cut the stalk crosswise, cook in salted water with a pinch of sugar until al dente. Drain and drain well.
Heat the oil in a pan, fry the sweet potatoes on all sides, add the Brussels sprouts, shallots, garlic and thyme, fry lightly. Pour in the balsamic vinegar, season with salt and pepper and serve sprinkled with the chopped parsley and cheese.