Heat a non-stick pan to medium heat and drizzle with olive oil. Add the sausage and cook for about 5-10 minutes until it is cooked through. Transfer to a plate.
In the same pan add the onion, tomato, salt, and pepper. Cook until the onion is transparent and the tomato slightly charred.
Meanwhile, in a mixing bowl whisk the eggs until frotty. Transfer to the pan and cook until cooked through on the bottom and slightly wet on top.
Add the sausage and cheese on one side of the omelette. Flip the other side on top and slide it onto a plate.