Whiskey-Cheese Fondue

In a bowl, toss the cheddar and Jack cheeses with the cornstarch. Rub the garlic cloves on the inside of a saucepan, then discard. Add the wine to the saucepan and bring to a simmer. Add the cheese mixture in 4 batches, whisking constantly over moderate heat and letting it melt completely between additions. Add the whiskey and stir just until the fondue begins to bubble, 3 minutes. Season with salt and pepper; serve hot with bread, breadsticks and carrots.