In a medium bowl, whisk together the flour, baking powder and salt to combine.
Using a fork, stir in the olive oil. Pour in the water, and using a wooden spoon, stir until the mixture forms a rough dough. Turn out onto a clean counter (you do NOT need to flour it beforehand). Knead the dough a few times until it becomes smooth.
Heat a cast-iron skillet over medium-high heat.
Divide the dough into eight equal pieces. Take a ball of dough and starting at the center, gently press it out into a circle using your fingertips.
Switch to a rolling pin and gently finish rolling it out into an 8-inch round.
Pierce the surface a few times with the tines of a fork. Repeat with the remaining balls of dough.
Place a formed piadina in the preheated skillet, and let it cook until golden with some dark or charred spots on the underside (it may also puff up a little).
Flip the piadina and cook until the other side is golden with a few dark spots as well.
Serve warm the sandwich fillings of your choice.