Preheat the oven to 375°F (190°C).
Bring a large pot of salted water to a boil. Add the broccoli florets and blanch for 2 minutes until bright green and slightly tender. Drain and set aside.
In a large skillet, heat 1 tablespoon of olive oil 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 and cook for 5-7 minutes, stirring occasionally, until the chicken is cooked through and no longer pink inside.
In a small bowl, whisk together the coconut milk, chicken broth, arrowroot starch, dried thyme, dried oregano, smoked paprika, sea salt, black pepper, and nutritional yeast until smooth.
Pour the coconut milk mixture into the skillet with the chicken and onions. Stir well and cook for 3-4 minutes until the sauce thickens slightly.
Add the blanched broccoli to the skillet and gently fold to combine all ingredients evenly.
Transfer the mixture into a greased 9×9-inch baking dish. Drizzle the remaining 1 tablespoon of olive oil over the top.
Bake in the preheated oven for 20 minutes until the casserole is bubbly and slightly golden on top.
Remove from the oven and sprinkle chopped fresh parsley over the casserole before serving.