Preheat your fondue pot to low (if using).
Prepare ingredients: drain and coarsely chop the 1/2 cup jarred artichoke hearts; finely chop or roughly chop the 2 1/2 cups spinach if the leaves are large; mince the 1 clove garlic; grate or chop the cheeses if not already grated (3 oz Gruyere, 1/2 cup shredded mozzarella, 1/3 cup grated Parmesan).
In a small saucepan combine the 3 ounce chicken broth, the chopped spinach, and the chopped artichoke hearts. Place the pan over medium heat.
Bring the mixture to a gentle simmer, stirring occasionally so the spinach wilts evenly.
Once the mixture is simmering, add the minced garlic and cook for 1 minute, stirring.
In a separate bowl toss the Gruyere, mozzarella, and Parmesan with the 1 tablespoon all-purpose flour until the cheeses are evenly coated.
Reduce the saucepan heat to low. Add the cheese-and-flour mixture to the pan in small additions, stirring constantly and allowing each addition to melt into a smooth mixture before adding more.
When all the cheese is fully melted and the dip is smooth and thickened, remove from heat.
Transfer the dip to the preheated fondue pot set on low (or keep in the saucepan over very low heat) and serve immediately.