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.