In a medium bowl, toss the freshly grated Gruyère and Emmentaler cheeses with the cornstarch until the cheese is evenly coated. This will help prevent the fondue from becoming lumpy.
Rub the inside of a fondue pot or a heavy-bottomed medium saucepan with the cut sides of the garlic clove. Pour in the white wine and lemon juice, and heat over medium-low heat until simmering gently; do not let it boil.
Gradually add the cornstarch-coated cheese to the simmering wine, a handful at a time, stirring constantly in a zigzag or figure-eight pattern with a wooden spoon until the cheese is completely melted before adding more. The mixture should be smooth and creamy.
Once all the cheese is incorporated, stir in the kirsch (if using), nutmeg, and white pepper. Continue to cook for another 2-3 minutes, stirring constantly, until the fondue is smooth and bubbling slightly.
Carefully transfer the pot to a lit fondue burner on the table. Serve immediately, using long-stemmed fondue forks to dip the bread cubes into the warm, melted cheese.