Heat a skillet over medium heat. Spread one tablespoon of softened butter onto one slice of bread. Place the bread, butter side down, into the hot skillet.
Spread one tablespoon of pesto across the top surface of the bread. Spread 1/4 cup of the Monterey Jack cheese across the pesto, then top the cheese with half of the turkey. Add another layer of cheese, this time using 1/4 cup of cheddar.
Spread one tablespoon of pesto across a new slice of bread, then one tablespoon of softened butter across the other side. Place the bread slice, pesto side down, onto the cheddar. Using a spatula, lightly press down on the sandwich.
Cook for 2-3 minutes, until browned on the bottom.
Flip the sandwich, and cook another 2-3 minutes until browned, and cheese is melted.
Repeat to make second sandwich.
Cut both sandwiches in half, and serve warm!