Clean the artichoke by removing the hardest outer leaves and cut in thin slices. Clean also the mushrooms and slice them not too thin.
Add the olive oil and the garlic to a medium-sized pan and let it brown for two minutes. Then add the artichoke and cook with the fire set low.
After 5 minutes, add the potato cut in pieces of about 1 cm, season with salt to taste, and let cook on low fire covered. After a few minutes, add a cup of water and let cook for 10 minutes or until the potato is soft. If necessary, add more water.
When the potato softens, add the mushrooms, stir and cover for 10 more minutes. When you see that the potato has formed a soft cream and water was absorbed, remove it from the stove and let it cool down.
Add an egg to the veggies and mix it well, then add also the mozzarella and the parmesan.
If you have a puff pastry large roll, you can add the filling in half of it and then fold the other half on top, while if you have puff pastry sheets, you can place two of them on top of each other and seal them using a fork on the edges.
Brush a thin layer of egg and milk on top and bake in a pre-heated conventional oven at 180°C (356°F) for 15 minutes.