In a small saucepan, sauté the garlic over medium heat until translucent and fragrant, about 2 minutes.
Add the white grape juice (or broth mixture) and stir to combine.
Add in the cornstarch, both cheeses, salt, pepper, and cooking Sherry (if using). Use a whisk to stir and fully combine as the cheese melts. Stir continuously to prevent burning.
Stir in the basil. If the fondue is too thick, add a bit more white grape juice. If too thin, add a bit more cheese.
Remove from heat and serve immediately. Use crostini, bread cubes, apples, veggies, or chips as dippers.
Enjoy! 😊