Evenly spread 1/2 tablespoon of softened unsalted butter onto one side of each slice of sourdough bread. These buttered sides will become the crispy exterior of your sandwich.
Place one slice of bread onto a clean surface with the unbuttered side facing up. Spread the 1 tablespoon of basil pesto evenly over this surface, ensuring it reaches close to the edges.
Distribute the 2 ounces of shredded low-moisture mozzarella cheese over the pesto layer. Try to keep the cheese contained within the perimeter of the bread to prevent excessive melting out into the pan.
Carefully place the second slice of bread on top of the cheese, ensuring its buttered side is facing outwards. Press down gently to secure the layers.
Heat a 10-inch nonstick skillet or cast-iron pan over medium-low heat for 2 to 3 minutes. This lower heat setting is crucial for achieving a deep golden-brown crust and allowing the cheese to melt thoroughly without burning the bread.
Carefully place the assembled sandwich into the preheated skillet. Cook for 3 to 5 minutes, or until the bottom slice is a rich golden brown and you can see the cheese beginning to soften around the edges.
Using a sturdy spatula, carefully flip the sandwich. Continue to cook for another 3 to 5 minutes, or until the second side is also golden brown and the cheese is completely melted and gooey.
Remove the finished grilled cheese from the skillet. For optimal enjoyment, let it rest on a cutting board for 1 minute before slicing it in half diagonally and serving.
Notes
Let it rest on a cutting board for 1 minute before slicing for optimal enjoyment.