Place the shredded Gruyere and Swiss cheese in a gallon-size resealable bag with the cornstarch and shake until evenly coated.
In a fondue pot, or in a regular saucepan, add chicken broth, lemon juice, and garlic and bring to a simmer. Reduce the heat to medium-low. Add the cheese, a small handful at a time, stirring constantly. Try using a wooden spoon and stir in an S-shaped motion, making sure to scrape the bottom of the pot so it doesn't burn.
Once the cheese is melted and begins to just barely simmer, add the remaining spices and move it immediately to the table and place on the fondue stand with flame below, if possible.
Arrange an assortment of bite-size dipping foods on a platter. Try steamed broccoli and/or cauliflower, carrots, apples, chicken sausages, bread, lightly sauteed mushrooms, tender potatoes - the options are endless.