Combine the grated Gruyère cheese, Swiss cheese, and Fontina cheese with the cornstarch, in a bag or bowl until evenly coated, and set aside.
Rub the inside of a fondue pot on the cut sides of the garlic cloves; discard the garlic.
In the fondue pot, add the 1 cup chicken stock, milk, and lemon juice and cook over medium-low heat, once warm, slowly add the cheese. Stir occasionally in a figure-eight motion, until the cheese melts, about 5 minutes. Don’t let the mixture boil.
Reduce heat to low. Add the ground nutmeg, ground pepper, sea salt, and paprika. Taste and adjust as needed. Add up to ¼ cup more chicken stock if needed to thin it out. Cook, stirring gently, until creamy and smooth, about 3 minutes; don't overcook the fondue or it will get stringy.
To serve, keep warm over low heat. Use long forks or skewers to dip bread, vegetables, potatoes, etc. into the melted cheese. Enjoy!