Preheat oven to 375F (190C). Prepare large and dip baking dish, set aside.
In a large bowl mix chicken breast, oil, salt, pepper and paprika.
In a large pan, heat oil, add seasoned chicken chunks and cook for 6-7 minutes, until cooked through. Remove from the pan.
To the same pan add 2 tablespoons of olive oil and heat over medium heat. add chopped onion and cook until slightly golden, about 5-6 minutes. Add crushed garlic, sliced mushrooms and cook for 5-6 minutes. Until the mushrooms are softened. Remove from the pan.
Make the sauce: In the same pan melt butter, add flour, whisk until smooth paste forms and cook for 1 minute. Gradually add warm stock and cream, while whisking constantly. Keep whisking over medium-high heat until the sauce is smooth and thickened. Stir in salt, pepper and nutmeg.
To the pan with the sauce add chicken chunks, broccoli florets and mushroom mixture. Mix until combined.
Pour the filling into prepared dish. Sprinkle shredded cheese on top.
Bake for about 20-25 minutes, until golden-brown and bubbly. Let cool slightly before serving.