Preheat the oven to 400 degrees F (200 degrees C).
Heat oil in a large skillet over medium heat. Add cabbage and cook for about 18 minutes. Stir in butter and season with salt. Continue cooking until cabbage is soft, about 2 minutes more.
Roll puff pastry out on a lightly floured surface into a large square. Place into a springform pan, allowing the corners to hang over the sides.
Beat egg and water together in a bowl and stir in Swiss cheese.
Pour cooked cabbage into the pastry-lined pan and cover with egg mixture. Fold pastry corners over filling and punch together in the middle.
Bake in the preheated oven until pastry is golden brown, about 25 minutes.
