Preheat the oven to 375°F (190°C).
Steam the broccoli florets until tender-crisp, about 4-5 minutes. Drain and set aside.
Heat olive oil in a medium skillet over medium heat. Add the chopped onion and cook until translucent, about 3-4 minutes.
Add the minced garlic to the skillet and cook for another 1 minute until fragrant. Remove from heat.
In a large mixing bowl, combine the shredded chicken, steamed broccoli, cooked onion and garlic, Greek yogurt, chicken broth, Dijon mustard, dried thyme, salt, and black pepper. Mix well until all ingredients are evenly incorporated.
Transfer the mixture to a greased 9×13 inch casserole dish and spread evenly.
In a small bowl, mix the sliced almonds, shredded cheddar cheese, and grated Parmesan cheese.
Sprinkle the almond and cheese mixture evenly over the top of the casserole.
Bake uncovered in the preheated oven for 25-30 minutes, or until the topping is golden brown and the casserole is heated through.
Remove from the oven and let it rest for 5 minutes before serving.