Place the sweet potato chunks in a saucepan. Cover with cold water and bring to a boil. Lower the heat and simmer until tender, about 10 to 15 minutes. Drain and transfer to a large bowl.
While the sweet potato is still warm, crumble the goat's cheese and shallots into the bowl.
Meanwhile, cook the bacon in a skillet. Set aside to drain on a plate lined with a paper towel. When cool, chop into bite-sized pieces. Add to the sweet potato and goat's cheese mixture.
Beat the eggs in a large bowl and add in the Parmesan, mixing well to combine. Season with salt and pepper.
Place an 8- or 9-inch nonstick frying pan over a medium heat and add the olive oil. Add the sweet potato mixture, distributing it evenly over the base of the pan. Pour in the beaten egg mixture, making sure it evenly coats the sweet potato mixture. Reduce the heat to low and cook for 8 to 10 minutes, or until the eggs on top are almost set.
Put the pan under a hot broiler for a few minutes to finish the frittata, until it's golden brown on top. (Remember to be careful when taking the pan out of the oven and for some time afterward, as the handle will be hot!) Don't worry if it's still a little soft or runny in the center, as it will continue to cook as it cools.
Loosen the frittata with a knife or spatula until it moves freely in the pan, then slide it out onto a platter or place a platter over the pan and invert. Cut the frittata into wedges to serve. This is best served at room temperature.