Heat the oven to 220 C / 425 F with racks in the upper and lower thirds. Line two 33 x 46 cm / 13 x 18 inch sheet pans with parchment.
Blend the cottage cheese, eggs, 1 tbsp olive oil, oregano and garlic powder in a 1.5 L / 6-cup blender or food processor for 30 to 45 seconds, until smooth. Pour into a mixing bowl, add the flour and baking powder, and stir until no dry streaks remain. The dough will be thick and sticky.
Rub the remaining 1 tbsp olive oil over your hands and the top of the dough. Divide the dough between the two pans and press each portion into a rough 28 x 38 cm / 11 x 15 inch rectangle about 4 mm thick. Bake for 14 minutes, swapping the pans between racks after 7 minutes, until the surface is set and the edges are golden. Press the center: it should spring back with no wet shine. If it dents or looks glossy, bake 2 minutes more, because an underbaked base turns gummy under the sauce.
Spread 75 g pizza sauce over each base, leaving a 2 cm border. Divide the mozzarella, chicken and red onion between the pans and lay the pepperoni on top. Bake for 10 minutes, swapping the pans after 5 minutes, until the cheese bubbles and browns in spots and the pepperoni edges curl.
Rest the pizzas on the pans for 3 minutes so the cheese sets. Scatter with torn basil and red pepper flakes, then cut each flatbread in half to make 4 servings.