Preheat your oven to 375°F (190°C). Lightly grease a 9 × 13-inch baking dish with olive oil or cooking spray.
Finely shred the cabbage and carrots. Dice the onion and mince the garlic.
Heat the olive oil in a large skillet over medium heat. Add the onion and cook for 2–3 minutes, until softened. Add the garlic and cook for another 30 seconds.
Add the shredded cabbage and carrots. Cook over medium heat for 6–8 minutes, stirring occasionally.
If the vegetables release a lot of liquid, continue cooking for another 1–2 minutes until most of the moisture has evaporated.
Add the cottage cheese, Greek yogurt, eggs, Dijon mustard, onion powder, garlic powder, smoked paprika, thyme, black pepper, and salt to a blender. Blend for approximately 30–45 seconds, until smooth and creamy.
Transfer the cooked cabbage and carrots to a large bowl. Pour the creamy mixture over the vegetables. Add ½ cup of the shredded cheddar and the Parmesan. Stir gently until everything is evenly coated.
Spread the mixture evenly into the prepared baking dish. Smooth the surface with a spatula.
Sprinkle the remaining ½ cup cheddar evenly over the top. Add dried dill, parsley, or red pepper flakes if desired.
Place the dish in the 375°F (190°C) oven. Bake uncovered for approximately 30–35 minutes.
For a deeper golden crust, switch the oven to broil for 1–2 minutes. Watch continuously because the cheese can brown quickly.
Remove the casserole from the oven and let it rest for 10 minutes.
Sprinkle with fresh parsley if desired. Serve warm alongside grilled chicken, turkey, fish, lean beef, or another protein-rich main course.
