Place the slices of sweet potatoes into a microwave safe dish, and add just enough water to cover. Cook for 10 minutes in the microwave, or until starting to become tender.
Preheat the oven's broiler. Place the sweet potato slices onto a greased broiler pan. Slice the feta cheese the best you can, and place a piece on top of each potato slice. Drizzle balsamic vinegar over all.
Place under the preheated broiler for about 6 minutes, or until cheese is lightly browned.