In a small bowl, combine the softened butter with garlic powder, and a pinch of salt and pepper. Mix well to create a garlic herb butter.
Spread the garlic herb butter evenly on one side of each slice of sourdough bread.
On the unbuttered side of two slices, layer the shredded cheddar and Gruyère cheese evenly. Sprinkle the fresh basil if using for added flavor.
Top with the remaining two slices of bread, buttered side facing out.
Place the sandwiches in the preheated skillet. Grill each side for about 3-4 minutes or until golden brown and the cheese has melted, pressing down slightly with a spatula for a crispier crust.
Once finished, remove the sandwiches from the heat and let them rest for a minute.
Cut each sandwich in half and serve hot.
Notes
For extra flavor, experiment with different cheese combinations.