Cook bacon in a skillet set over medium heat until crisp.
Lightly toast the interior of the croissant while bacon cooks.
Beat eggs in a small bowl and add a pinch of salt.
While bacon is cooking set a medium non-stick skillet over high heat and add butter. Once foaming add beaten eggs and swirl around the pan into a thin layer. Use a spatula to gently lift up the edges of the egg and tilt the pan to allow uncooked eggs to fill the void.
Once the top of the eggs are almost cooked thru, use a spatula to fold the egg in half, and then in half again, so it is in quarters. Remove from heat and top with a slice of cheese.
Place the folden egg on the bottom slice of the croissant and top with bacon. Add the top half of the croissant and serve.
Notes
If you are making these breakfast croissants for a larger crowd and need to prepare them in batches, the finished croissant sandwiches can be kept warm by placing them on a baking sheet in an oven set to 200 degrees.