Preheat air fryer to 350 degrees F.
In a small bowl, stir together the melted butter, garlic, and chives.
Using a bread knife, cut slits into the top of the bread loaf in a grid pattern. Do not slice all the way through the bread.
Use a small brush or a spoon to coat all the slits with the butter mixture, getting as much butter as you can down into the cracks.
Slice the brie cheese into small wedges and press it down into each slit.
Sprinkle cheddar and mozzarella cheese over the top of the bread, filling any remaining slits with the shredded cheese.
Place bread loaf in preheated air fryer basket. Cook at 350 degrees F for 4-5 minutes until the cheese is melted and the bread is warmed through.