Preheat oven to 400°F.
In a pot of boiling salted water, par-cook the noodles for about 5 minutes, only until they are still very al dente. Drain and set aside.
Peel and mince the garlic. Rinse the chicken breast fillets, pat them dry, and cut into approximately ¾-inch pieces. Remove any tendons.
Heat the olive oil in a skillet. Sauté the garlic until translucent, then add the chicken. Cook for 5 minutes until golden brown. Season with salt and pepper.
Deglaze the pan with the heavy cream and vegetable broth and let the sauce simmer for about 6 minutes over medium heat.
Spread the noodles in the casserole dish and pour the sauce evenly over them. Season once more with salt and pepper.
Finally, top the shredded cheese on top and bake for about 20 minutes. The casserole is ready when the cheese is golden brown.
Remove the casserole from the oven, portion it onto plates, and sprinkle with chopped parsley.