Preheat the oven to 400°F (200°C).
In a medium bowl, beat the cream cheese until smooth. Stir in 1/4 cup cheddar, 1/4 cup Monterey Jack, the mayonnaise, and the pressed garlic until evenly combined.
Place the thin chicken breasts in an oven-safe baking dish and season both sides with salt and black pepper.
Spread the cheese mixture over the top of each chicken breast in an even layer.
Sprinkle the remaining cheddar and Monterey Jack evenly over the cheese-topped chicken.
Bake in the preheated oven for 20–30 minutes, or until the internal temperature of the chicken reaches 165°F (74°C) and the cheese is bubbly.
Garnish with chopped parsley and/or green onions, then serve hot.
