Heat half the butter and the oil in a medium non-stick frying pan. Add the onion and mushrooms and cook over medium heat, for 3-4 minutes or until onion is cooked and mushrooms golden. Remove from pan and place on a warm plate. Wipe out pan with kitchen towel.
Whisk the eggs and milk or cream in a bowl and season with salt and black pepper
Reheat the pan over medium heat. Add the remaining butter, allowing it to melt. Swirl the butter around the pan to evenly coat. Add the egg mixture to the pan, and as it begins to cook use a wooden spoon to push cooked parts from the edge to the centre of the pan. Allow the uncooked egg mixture to flow into empty spaces.
When the egg is nearly cooked, sprinkle with the grated cheddar. Cook for another 1-2 minutes as the cheese melts. Top with the cooked mushrooms and halved tomatoes. Fold the omelette in half and slide onto a warm serving plate. Sprinkle with basil leaves and cut in half to serve 2 people.
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