Preheat oven to 415°F and allow to fully preheat before vegetables go in — high temperature is essential for proper caramelization on broccoli and onion.
Cut broccoli into florets approximately 1 to 1.5 inches — noticeably smaller than usual — smaller florets have more surface area in contact with hot pan cook faster and develop more caramelized edges per piece.
Place small broccoli florets, quartered yellow onion, and whole peeled garlic cloves in a single layer in a large oven-safe baking dish or sheet pan.
Drizzle 1–2 tablespoons olive oil over vegetables and toss to coat everything evenly.
Sprinkle dried oregano, red chili flakes, salt, and black pepper over vegetables and toss again.
Place full block of feta cheese in one corner of the baking dish alongside the vegetables — it will roast and develop its own golden crust.
Roast on center rack at 415°F for approximately 30 minutes until broccoli is roasted and slightly crispy at edges, onion is caramelized and tender, garlic is golden and mellow, and feta has developed a golden crust — check after 20 minutes as oven temperatures vary.
Transfer all roasted vegetables garlic and feta from baking dish into a high-powered blender.
Add bone broth, full-fat cottage cheese, fresh baby spinach, lemon zest, and lemon juice to the blender.
Blend on high speed until completely smooth and creamy with no visible vegetable pieces spinach or cottage cheese curds remaining — blend in batches if blender is small and combine in a pot.
Finished soup should be silky and a deep vibrant green color.
Transfer blended soup to a saucepan and warm over medium heat stirring frequently until heated through to preferred serving temperature.
Taste and adjust seasoning — add more salt if needed more lemon juice for brightness or more chili flakes for additional heat — this final seasoning adjustment makes the difference between a good soup and a great one.
Ladle hot soup into bowls and garnish each with fresh dill sprigs a pinch of additional red chili flakes and a generous scatter of finely shredded Manchego or Parmesan cheese.
Serve immediately.