Preheat oven to 450Â°F with a heavy baking sheet on rack in middle.
Stir together flour, chopped rosemary, baking powder, and salt in a medium bowl. Make a well in center, then add water and oil and gradually stir into flour with a wooden spoon until a dough forms. Knead dough gently on a work surface 4 or 5 times.
Divide dough into 3 pieces and roll out 1 piece (keep remaining pieces covered with plastic wrap) on a sheet of parchment paper into a 10-inch round (shape can be rustic; dough should be thin).
Lightly brush top with additional oil and scatter small clusters of rosemary leaves on top, pressing in slightly. Sprinkle with sea salt. Slide round (still on parchment) onto preheated baking sheet and bake until pale golden and browned in spots, 8 to 10 minutes. Transfer flatbread (discard parchment) to a rack to cool, then make 2 more rounds (1 at a time) on fresh parchment (do not oil or salt until just before baking). Break into pieces.
Flatbread can be made 2 days ahead and cooled completely, then kept in an airtight container at room temperature.