Preheat the oven to 375°F (190°C).
Bring a large pot of water to a boil. Add the broccoli florets and blanch for 2 minutes until bright green and slightly tender. Drain and set aside.
Heat olive oil in a large skillet over medium heat. Add the chopped onion and cook for 3-4 minutes until translucent.
Add the minced garlic to the skillet and cook for 1 minute until fragrant.
Add the chicken pieces to the skillet. Season with salt, black pepper, dried thyme, and smoked paprika. Cook for 6-8 minutes, stirring occasionally, until the chicken is cooked through and no longer pink inside.
In a large mixing bowl, combine Greek yogurt, cottage cheese, chicken broth, Dijon mustard, and shredded cheddar cheese. Stir until smooth.
Add the cooked chicken, sautéed onions and garlic, and blanched broccoli to the mixing bowl. Mix gently to combine all ingredients evenly.
Transfer the mixture into a greased 9×13 inch casserole dish and spread evenly.
Sprinkle the grated Parmesan cheese evenly over the top of the casserole.
Bake in the preheated oven for 25 minutes or until the casserole is bubbly and the top is golden brown.
Remove from the oven and let cool for 5 minutes before serving.