Shred the sweet potatoes and chop the green onions. Mix them together and add the oil, salt and pepper. Press into individual casserole dishes or larger dishes.
Bake for 45 minutes until the sweet potatoes start to brown.
Break eggs over the sweet potatoes, and sprinkle parmesan cheese on top. Return to the oven for 5 more minutes, or slightly longer if you don't want the yolks to be runny.