Vigorously rub the inside of a fondue pot or a 2-quart saucepan with garlic; and discard. Add the Sauternes, and bring to a boil over medium heat.
Meanwhile, in a small bowl, stir to combine the Stilton and cornstarch. Once the Sauternes has come to a boil, slowly add the Stilton mixture, while whisking constantly. Be sure each addition is completely melted and incorporated before adding more. Once all of the cheese has been added, cook for 1 minute more. Whisk in creme fraiche, and season with salt and pepper. Remove from heat, and serve immediately with bread, potatoes, beef tips, or pickled vegetables, as desired.