Peel the potato/rutabaga and onion. Cut the potato/rutabaga in to relatively thin disks - this is probably easiest if you cut chunks around 1in/2.5cm square or a bit smaller then slice them around ⅛in/3mm thick. Peel and dice the onion.
Heat the oil in a small skillet/frying pan over a medium heat then add the potato/rutabaga and onion. Cook, stirring regularly to move the bottom pieces to the top and prevent browning for around 20min, until the potato/rutabaga slices are soft to the knifepoint.
Beat the eggs in a medium bowl and season with salt and pepper. Add the cooked potato/rutabaga and onion and mix through.
Add a little more oil to the skillet if it is dry then tip in the egg mixture and cook over a medium-low heat until you can see it has cooked round the outside and is fairly set in the middle. Heat the broiler/grill and put the pan under until the top is fully set - you aren't looking for it to brown too much, just set the egg.
Allow to rest slightly before loosening from the pan, then place a plate over the pan and invert onto the plate. Serve warm or room temperature in slices or cubes.
Video
Notes
Note - if using potatoes, I find it helps to put the slices of potato in a bowl of water as you cut them to help save them from browning and remove some excess starch. Pat the slices dry before adding to the skillet.