Pierce the skin of the sweet potatoes three or four times with a fork, and then either cook in the microwave (on high, for 7-8 minutes) or the oven (for 20-30 minutes) until very soft and tender. Set aside.
Meanwhile, heat the olive oil in a large skillet over medium-high heat. Add in the garlic and onion, and cook until just tender and fragrant, about three minutes.
Add in the mushrooms and sweet peppers, plus salt and pepper, and cook until all vegetables are tender, about eight minutes.
Slice the cooked sweet potatoes lengthwise, and use a fork to fluff up the flesh. Place each fluffed sweet potato in a baking dish.
Spoon the mushroom filling into each sweet potato, heaping on top. Sprinkle the cheese on top of the sweet potatoes.
Bake in preheated oven for 7-10 minutes, or until the cheese is bubbly.