Combine 1 3/4 cups flour, 1 tablespoon rosemary, baking powder, and 3/4 teaspoon salt. Add water and 1/3 cup olive oil; stir until dough is well combined.
Sprinkle a work surface with 2 teaspoons flour. Turn dough out onto the surface and knead until smooth, 6 to 8 turns. Divide dough into 3 sections; keep covered with plastic wrap while shaping flatbreads.
Shape each third on a sheet of parchment paper; flatten into a thin round 10 to 12 inches thick. Brush lightly with about 1/2 teaspoon olive oil. Sprinkle lightly with sea salt and garlic powder. Press thin clusters of rosemary into the dough. Repeat shaping and coating the remaining dough sections; place them on a baking sheet.
Bake in the preheated oven until beginning to brown, 12 to 14 minutes. Cut with a pizza knife immediately or let cool and break into pieces.