Preheat the oven to 375°F (190°C).
Bring a large pot of water to a boil. Add the broccoli florets and cook for 3 minutes until bright green and slightly tender. Drain and set aside.
In a large skillet, heat olive oil over medium heat. Add the chopped onion and cook for 3-4 minutes until translucent.
Add the minced garlic and cook for 1 minute until fragrant.
Sprinkle the flour over the onion and garlic mixture, stirring constantly for 1 minute to create a roux.
Gradually whisk in the chicken broth, stirring continuously until the mixture thickens, about 2-3 minutes.
Remove the skillet from heat and stir in the Greek yogurt, Dijon mustard, black pepper, salt, and paprika until smooth.
In a large mixing bowl, combine the shredded chicken, cooked broccoli, cottage cheese, cheddar cheese, mozzarella cheese, and the sauce from the skillet. Mix well to combine.
Transfer the mixture into a greased 9×13 inch casserole dish and spread evenly.
Sprinkle the grated Parmesan cheese evenly over the top.
Bake in the preheated oven for 25-30 minutes, until the casserole is bubbly and the top is golden brown.
Remove from the oven and let it rest for 5 minutes before serving.