In a large bowl, sift together the flour, baking powder and salt, then make a well in the centre. Mix the water, milk and extra virgin olive oil. In a separate bowl, pour the wet ingredients into the dry, bit by bit, until combined. Knead until a smooth, elastic dough forms that is moist without being sticky (you may need to add a touch more water), about 15 minutes. Wrap tightly in cling film and allow to rest at room temperature for at least 1 hour, or ideally overnight in the fridge (remembering to allow it to return to room temperature before rolling out).
Split the dough into 10, and using a rolling pin, roll out each piece to about 3mm thick on a floured surface. Heat a heavy bottomed non-stick pan to medium heat. Dust off the excess flour and cook the bread one side for 1-2 minutes, or until the base is lightly golden. As any air bubbles form, pierce them with a fork to ensure the bread stays flat.
Flip the bread and turn the heat down to low. Cover half the bread with the sliced stracchino and prosciutto, then fold over to form a semi-circle shape. Continue to cook until lightly browned on one side, then flip to cook the other side. The filling should now be warm and the cheese melted.
Cut into quarters and serve immediately with some dressed rocket.