Slice the rutabaga on both ends to make them flat. Turn the rutabaga on one of the flat ends, so it is stable. Using a sharp chef’s knife, peel the hard, waxy skin off of the root. Turn the rutabaga onto the other flat end and trim any spots that you may have missed.
Use a mandolin to slice the rutabaga into thin ⅛” slices. My favorite mandolin to use is Japanese, as it is lightweight and sharp. If you do not have a mandolin, you can use a very sharp chef’s knife and good knife skills to cut the root into thin slices.
Heat a 10” nonstick skillet over medium-high heat until it is starting to get hot. The pan does not have to be super hot for this step. Fill the pan with olive oil. Add in the sliced rutabaga. Season the rutabaga with ½ tsp sea salt. Then stir the rutabaga well to incorporate the seasoning. Cook the rutabaga on low heat, so the olive oil does not smoke. Cook the rutabaga in this manner for 15-17 minutes until softened. Be sure to stir the rutabaga occasionally.
While the rutabaga is cooking, slice a white onion into julienne pieces. Drain about 1-2 teaspoons of olive oil from the rutabaga pan into it. Heat the pan over medium-high heat until hot. Add in the onion and cook until it is starting to brown, stirring occasionally. Add a pinch of salt. As soon as the onion begins to brown, add in about 1-2 tablespoons of water. Then continue cooking until the water evaporates and the onion starts to brown again. Repeat this process several times, cooking for a total of 10-12 minutes until the onion is nicely browned.
Preheat the oven to 350 F. Scramble the eggs in a bowl. Add ¼ teaspoon of sea salt. Whisk well and set aside.
Top the rutabaga with the caramelized onions and then the beaten eggs. Cook the mixture on the stove until the bottom is starting to brown and the edges are puffy. There will be some liquid left in the center of the tortilla but that is ok because the omelette will go into the oven to finish cooking.
Place the skillet into the oven and cook for 10-12 minutes until the omelette is cooked through. Carefully flip the omelette onto a serving platter. Cut it into 8 pieces.