Combine sake, butter, and garlic into a saucepan over medium heat. Cook and stir until the mixture has thickened and reduced in volume by one half, about 3 minutes. Add cream to the sake mixture; stir until reduced by one fourth, about 3 minutes. Season with basil, parsley, and salt and pepper.
Stir Gorgonzola cheese and Parmesan cheese slowly into the sake mixture; simmer and stir continuously until smooth, about 3 minutes. Simmer until flavors combine, about 5 minutes.