Preheat a 2-cavity waffle iron for about 5 minutes or until hot.
While the waffle iron is preheating, lightly whisk the eggs and vanilla extract in a medium bowl. Using a fork or a rubber spatula, mix in the shredded mozzarella.
Brush the two waffle iron cavities with 1 tablespoon of melted butter. Brush the top and bottom parts.
Pour ¼ of the mixture (about ½ cup) into each cavity.
Cook the chaffles until browned and crispy, 5-7 minutes. Start checking after 5 minutes.
Remove the cooked ones to a baking dish and place them in the oven to keep warm.
Brush the waffle iron cavities with the remaining butter. Give the remaining mixture another stir, then pour it into the waffle iron's cavities, dividing it evenly. Cook until browned, about 5-7 minutes.
I don't add any sweetener because I drizzle the chaffles with sugar-free maple syrup.
Chaffles tend to stick to waffle makers more than other waffles, so make sure your waffle iron is truly nonstick and generously grease it. If they stick, gently release them from the waffle iron by sliding a cake server or a dinner knife around their edges and then sliding a wide spatula underneath them.
You can keep the leftovers in an airtight container in the fridge for up to 4 days. Reheat them in a toaster on the lowest setting. You can also freeze the cooled leftovers in a freezer bag. Separate them with wax paper squares to prevent them from sticking together.