Preheat the oven: Preheat your oven to 375°F (190°C).

Cook the leeks and garlic: In a large skillet, melt the butter over medium heat. Add the sliced leeks and cook for 5-7 minutes until softened. Add the minced garlic and thyme, cooking for another 1-2 minutes until fragrant.

Prepare the sauce: Stir in the heavy cream and chicken broth, bringing the mixture to a simmer. Let it cook for 3-4 minutes, stirring occasionally, until the sauce thickens slightly. Season with salt and pepper.

Assemble the bake: In a greased baking dish, layer the shredded chicken at the bottom. Pour the creamy leek sauce over the chicken and spread it evenly. Sprinkle the shredded cheddar cheese on top.

Bake: Bake the casserole in the preheated oven for 20-25 minutes, or until the top is bubbly and golden brown.

Serve: Garnish with fresh parsley and serve hot. This dish pairs well with a side of steamed greens or cauliflower mash.