This is probably the most important part of making this dish–the size of the hole. You want the hole big enough to hold the egg and fry it in the bread but not SO big that it doesn’t fill the hole. Making the hole too small has the opposite affect, and the egg overruns.
Add the butter to your frying pan and melt it over a medium-high heat. I add in the bread and toast both sides before adding the egg, but this isn’t required. It is just a preference. If you do this, you might need a bit more butter for frying the egg itself.
Crack the egg into the “basket” and let it cook until the white are set. Or you can flip it.
Place the asparagus in a steamer and steam 3-5 minutes. You want it crisp tender.
Take your slice of bread, pile on the 5 spears of asparagus and the 1/3 cup of Gruyere. Place it on a parchment-lined baking sheet and put it in the broiler until the cheese fully melts. This should take about 2 minutes or so.
When the cheese is melted and the Egg in the Basket is made, transfer the bottom half of the sandwich to the frying pan, melting the butter in the pan first.
Fry it all up, carefully flipping it to melt the cheese into the Egg in a Basket.