Rub cut faces of garlic cloves around the inside of a fondue pot, double boiler, or stainless steel mixing bowl set over a pot of simmering water (do not allow bowl to come into direct contact with the water).
Add wine and heat until steaming.
Meanwhile, in a large bowl, toss together both cheeses with cornstarch until evenly coated.
Working over low heat, add cheese a handful at a time, stirring until mostly melted before adding next handful.
Continue until all cheese is melted into the wine, forming a smooth, glossy melted cheese sauce, about 10 minutes; it is very important that the fondue stay below a simmer once you start adding the cheese, or there's a risk it could break.
Stir in lemon juice and kirsch, if using, until fully incorporated.
Season with salt and pepper.
If not already in a fondue pot, transfer fondue to a fondue pot to keep it warm and melted at the table.
Serve with toasted bread cubes and lightly blanched vegetables for dipping.
If fondue begins to thicken too much, add a small splash of wine to loosen it.
