Rub the inside of a fondue pot with the clove of garlic; set aside.
In a heavy pot over low heat, add the wine and bring it to a low simmer. In a small bowl, whisk together the cornstarch, kirsch, dry mustard and lemon juice; set aside.
Gradually add the grated cheese to the wine and stir with a wooden spoon (it's better to stir in a z-shaped pattern instead of a circular pattern). When cheese is just melted, add the cornstarch mixture to the pot and stir to combine.
Bring the fondue to a low simmer and stir until thickened, about 3-5 minutes.
Transfer to fondue pot and light the flame underneath the pot.