Combine flour and salt with ¾ cup plus 2 tbsp warm water and 3 tbsp oil in an electric mixer with a paddle attachment on low speed. Increase speed to medium and knead until a dough forms and pulls away from the sides of the bowl (about 10 minutes). Add more flour if the dough is too sticky (up to 3 tbsp).
Turn dough out onto a lightly floured surface, coat your hands with flour and knead until smooth. Cover with plastic wrap and rest at room temperature for 2 hours.
Preheat oven to 225C. Halve the dough and roll out each half as thinly as possible into 30cm x 45cm rectangles (it should be translucent). Place a rectangle carefully onto a lightly oiled baking tray large enough to fit it without folding in edges. Tear stracchino into cherry-sized pieces and arrange over the dough at regular intervals, leaving 2cm around the edge. Carefully place the other rectangle of dough on top and press down lightly, ensuring the edges are flat, not crimped. With a pinching motion, tear a dozen small steam holes into the top sheet of dough at regular intervals between the cheese pieces.
Drizzle remaining olive oil over the top, season with salt, then bake in the middle of the oven until the edges are golden (20-25 minutes). Cut into squares and serve hot.