Heat oil in a non-stick pan over medium-low heat until the oil thins and ripples. Sauté onion until softened but not brown. Add eggs, allowing them to coat the bottom of the pan and cook, roughly 1 minute. Add spinach, cover with cheese, and cover pan. Cook on low heat until eggs are almost firm, then fold one half of the omelette over the other. Remove from heat and allow to set for 5 minutes before serving.