Rub the inside of a fondue pot with the crushed clove of garlic and discard the clove.
Add the chicken stock to a saucepot,* whisk in the mustard and bring it to a boil over medium-high heat.
While the chicken stock is coming to a boil, combine the cornstarch and white wine in a small bowl, stirring to dissolve the cornstarch and prevent lumping.
Once the chicken stock has come to a boil, add the white wine and cornstarch mixture while whisking. Bring that mixture back to a boil and cook for one minute, whisking constantly.
Remove the pot from the heat and whisk in the shredded cheese, stirring to make sure all the cheese melts.