Toast the croissants cut-side down in a dry skillet over medium-low heat for 2 minutes, then transfer them to plates.
Warm the ham in the skillet for 1 minute per side without browning it hard.
Whisk the eggs with salt and black pepper until no streaks remain.
Melt the butter in a 10-inch nonstick skillet over medium-low heat, add the eggs and pull the set edges toward the center until the sheet reaches 160°F.
Fold the egg sheet into a rectangle and cut it into four portions.
Fill each croissant with ham, folded egg and one Swiss slice, then warm the closed sandwiches for 2 minutes in a 300°F oven.