Add the cottage cheese to a food processor or blender and process for about 30 seconds, scraping down the sides as needed, until completely smooth. This creates a more uniform dough without noticeable cottage cheese curds.
Add the flour, baking powder, salt, and garlic powder to the blended cottage cheese. Pulse until the mixture comes together into a soft, slightly shaggy dough.
Transfer the dough to a lightly floured surface and knead gently for 1–2 minutes until smooth. Shape it into a ball, cover with a clean kitchen towel, and let it rest for 10 minutes to make rolling easier.
Divide the dough into 4 equal portions. Roll each piece into a thin circle or oval about 6 inches wide. Keep the flatbreads fairly thin so the centers cook through without becoming doughy.
Preheat the oven to 400°F and line a baking sheet with parchment paper. Arrange the rolled flatbreads on the sheet and lightly brush the tops with olive oil.
Bake for 12–18 minutes, checking around the 12-minute mark. The flatbreads are ready when the edges are golden, the centers are set, and they have puffed slightly.
Remove the flatbreads from the oven and let them cool for a few minutes. They will become slightly crisp around the edges as they cool while remaining tender enough to fold or use as wraps.