In a large mixing bowl or a bowl of a stand mixer, combine flour(s), baking powder and salt. Add the vegetable shortening and mix until the mixture is crumbly.
Add the water; mix and knead until a smooth and soft dough forms. Cover and set aside for for about 30 minutes.
When ready to cook, divide the dough into 3~4 equal size pieces (3 pieces for large piadine and 4 for smaller ones). Shape each piece of dough into a roll and cover.
Roll each piece into 8~9" round flatbread. Place it on a hot griddle and cook on medium-high flame for 1~2 minutes on both sides until brown spots form. Transfer the cooked piadina to a clean dishtowel and keep covered. Repeat with the remaining dough.
To make the Piada Sandwich: Place roasted vegetables, greens and cheese sauce on one half of the piadine, fold and serve right away.