Heat the olive oil in a skillet over medium-high heat and cook the mushrooms with 1/4 teaspoon salt for 7 minutes until browned and dry.
Transfer the mushrooms to a plate and whisk the eggs with the remaining salt and black pepper.
Melt the butter in a nonstick skillet and cook the eggs as one thin sheet until they reach 160°F.
Fold the egg sheet into a rectangle and cut it into four portions.
Fill each croissant with mushrooms, folded egg and one Swiss slice.
Warm the sandwiches in a 300°F oven for 2 minutes until the cheese softens.
