Begin by slicing the chanterelle mushrooms into uniform, bite-sized pieces. In a large skillet over medium-low heat, melt the butter and sauté the garlic for approximately 2 minutes, allowing the aroma to develop. Introduce the sliced mushrooms to the pan, cooking them thoroughly for about 7 minutes over medium heat until they are tender and slightly golden. Pour in the heavy whipping cream and incorporate the Parmesan cheese, stirring gently to form a cohesive, velvety sauce. Allow the mixture to simmer on low heat for an additional 5 minutes to thicken slightly and meld the flavors. If desired, stir in about 8 oz of your preferred cooked pasta to transform the sauce into a hearty main dish.