Preheat the oven to 350°F. Using buttter, grease the casserole dish.
Cut the chicken breast fillets into bite-sized pieces, then season them with salt and pepper. In a pan, heat olive oil and fry the chicken until evenly golden brown. Remove the chicken from the pan and set aside.
Peel the carrots, onions, and garlic. Thinly slice the carrots and dice the onion and garlic. Sauté the onion and garlic in the same pan until translucent and fragrant. Add the carrots and cook for 5 minutes over medium heat.
In a bowl, combine the heavy cream and milk. Season with salt, pepper, and dried thyme.
Add the cooked chicken and carrots to the prepared casserole dish. Pour the cream and milk mixture over the top and top with the grated cheese.
Bake for 30 minutes, or until the cheese is golden brown and crispy. Enjoy!