Preheat the oven to 350 F.
Bring a medium pot of unsalted water to a boil.
Cut swiss chard stems into 1/4-inch pieces and leaves into bigger chunks. Cook until tender, about 10 minutes.
In the meantime, thinly slice the onion.
Heat olive oil in a sauté pan and fry onion slices until soft and translucent.
Once swiss chard is ready, drain in a colander and squeeze out any extra liquid with a spoon. Transfer it into the pan together with the onion, toss for a couple of minutes and turn off the heat.
Add Ricotta cheese, Parmesan cheese, a dash of salt and pepper, and 3 of the eggs. Mix everything together.
Place puff pastry into a 10-inch baking pan or pie plate.
Pour in the vegetable and cheese mixture into the baking pan, and even the surface with the help of a wooden spoon.
Finally, beat the remaining egg and brush it on top of the quiche.
Bake for 30 minutes or until the crust turns golden brown.