Whisk the eggs, flour, salt, and pepper in a bowl until combined.
Shred the onion using the large holes of a box grater or the grating attachment of a food processor.
Shred the sweet potatoes using the large holes of a box grater or the grating attachment of a food processor.
Working in batches, place the sweet potatoes and onions in a dish towel, and squeeze out as much excess liquid as possible. Add the sweet potatoes and onions to the egg mixture, and toss with your hands to combine.
Heat oil in a skillet over medium heat. Once oil is hot, drop the potato batter into the pan by the heaping spoonful, keeping the pancakes about two inches apart.
Flatten each latke with the back of a spoon and cook until golden brown, two to three minutes per side. Transfer to a paper towel-lined tray to drain, then drizzle warm latkes with balsamic vinegar. Serve with a side of brie cheese.