Add the cottage cheese to a blender or food processor and blend for 30–60 seconds, stopping to scrape down the sides if needed. Continue blending until the texture is completely smooth and creamy with no visible curds, similar to a thick sauce.
Transfer the blended cottage cheese to a large mixing bowl. Add the eggs and Greek yogurt, then whisk thoroughly until the mixture is fully combined and uniform in color and consistency, with no streaks of egg remaining.
Sprinkle in the garlic powder, onion powder, salt, and black pepper. Add the shredded cheese and gently mix with a spatula or spoon until everything is evenly distributed without overmixing.
Add the chopped broccoli to the bowl and carefully fold it into the mixture, making sure the broccoli is spread evenly throughout so each slice will have a balanced amount.
Pour the mixture into a greased baking dish and use a spatula to smooth the top into an even layer, gently tapping the dish on the counter to release any air pockets.
Place the dish in the preheated oven and bake until the center is fully set and no longer jiggly, and the top is lightly golden. A knife inserted into the center should come out mostly clean.
Remove the dish from the oven and let it cool for 5–10 minutes before slicing. This resting time helps the bake firm up, making it easier to cut and serve neatly.