In a medium bowl, vigorously beat the eggs, salt, pepper, and red pepper flakes with a whisk or fork. You want the eggs to become frothy; it could take as long as 5 minutes. This step is important because it puts lots of air in the eggs and makes the finished omelet fluffier.
In a second bowl, combine the cheese, tomatoes, bacon, and basil.
Heat the olive oil in an oven-safe 12-inch skillet over medium heat.
Add the beaten eggs and cook gently, tilting the pan so that the uncooked egg slides under the more cooked parts. After 2 to 3 minutes, the eggs will begin to set.
Sprinkle the cheese and toppings mixture evenly over the eggs and remove the pan from the heat.
Transfer the pan to the oven and cook for 3 to 4 minutes, until the cheese melts.
Slide the omelet onto a serving plate, folding it over on itself as you do.
Let it sit for a couple of minutes, then cut in half and serve.