In a mixing bowl, whisk together the flour, salt, sugar, chopped rosemary, and parmesan cheese. Add the olive oil and stir it in with a fork until the mixture looks crumbly. Pour in the water a little at a time, mixing after each addition, until the dough just comes together into a rough ball. Avoid overmixing, since that can make the crackers tough instead of crisp.
Turn the dough out onto a lightly floured surface and knead it gently for about 30 seconds, just enough to bring it together smoothly. Shape it into a flat disc, wrap it, and let it rest at room temperature for 10 minutes. This short rest relaxes the dough so it rolls out easily without springing back.
Preheat your oven to 450 degrees Fahrenheit. On a well-floured surface, roll the dough out to about one-eighth inch thick. Rolling it thin is the secret to that shatteringly crisp texture, so take your time here and keep dusting with flour if it sticks.
Using a pizza cutter or sharp knife, cut the rolled dough into small squares or rectangles, roughly one and a half inches across. Transfer them to your parchment-lined baking sheet, leaving a little space between each one, then prick the center of each cracker with a fork so they bake flat instead of puffing up.
Sprinkle the tops of the crackers lightly with extra grated parmesan and a pinch of flaky salt. Press gently so the topping sticks to the dough before it goes into the oven.
Bake the crackers for 10 to 12 minutes, watching closely toward the end since the high heat can brown them quickly. They're ready once the edges turn golden and the cheese on top just starts to bubble and brown.
Let the crackers cool completely on the baking sheet before moving them. They crisp up further as they cool, so resist the urge to stack them warm.