Preheat the oven to 450 degrees . In a large bowl, toss the potatoes and oil. Sprinkle generously with salt and arrange in a single layer on a parchment-paper-lined baking sheet. Roast, turning once, until browned.
Meanwhile, in a medium bowl, mix together the cheese and cornstarch. Rub the cut sides of the garlic on the inside of a fondue pot or heavy 2-quart saucepan; discard the garlic. Add the wine and lemon juice and bring to a boil over medium heat. Cook for 1 minute. Gradually whisk in the cheese mixture, then cook for 1 minute. Stir in the nutmeg and season with salt and pepper. Serve warm with the roasted potatoes for dipping.