Heat oil or butter in omelet pan over medium heat. Add cherry tomatoes, cut side down, in two rows of four on one side of the pan. Beat eggs vigorously, until they start to foam. Carefully pour eggs into pan without disturbing tomato arrangement. As omelet cooks, lift edges and tilt pan to spread uncooked egg onto pan bottom. After about 1 to 1-1/2 minutes, add cheese and basil to tomato side of omelet. Then flip other side over the cheese and basil and let cook another minute. Plate the omelet cherry side up; garnish with basil leaf.
This recipe can be modified to accommodate more servings (i.e., 4 eggs, 6 eggs).