Preheat your oven to 375°F (190°C).
In a large skillet, heat olive oil over medium heat and sauté onions until soft.
Add minced garlic and sauté for another minute until fragrant.
Stir in the shredded chicken, broccoli florets, coconut milk, salt, pepper, and thyme.
Cook over medium heat for about 5-7 minutes until the broccoli is slightly tender.
Transfer the chicken and broccoli mix to a baking dish.
Sprinkle gluten-free breadcrumbs evenly on top.
Bake in the preheated oven for 25-30 minutes or until the top is golden.
Remove from the oven and let it cool for 5 minutes before serving.