Preheat a skillet over medium heat.
Mix the butter, garlic, and oregano in a small bowl.
Slice the buns in half and spread the garlic butter on the insides.
In a separate bowl, mix shredded chicken with mayonnaise, salt, and pepper.
Spoon the chicken mixture evenly onto one side of each bun.
Top with shredded mozzarella and cheddar.
Close the sandwiches and place them in the skillet.
Press gently and cook for about 3-4 minutes per side until golden and cheese is melted.
Remove, let them cool for a minute (if you can wait), and serve!