Separate the egg white from the yolk, keeping the yolk intact.
In the same skillet, heat a little more olive oil over medium-low heat.
Pour in the egg white, letting it cook for a few moments until it starts to set. Flip and then carefully place the bagel lid (the top half of the bagel) directly on top of the egg white in the skillet.
Gently place the egg yolk in the center of the egg white, on top of the bagel lid.
Cover the skillet with a lid and steam for 5 minutes, until the yolk is warm but still runny.