Preheat your grill or grill pan over medium heat.
In a small bowl, mix together garlic powder, onion powder, paprika, salt, and pepper. Rub this spice mixture onto both sides of the chicken breasts.
Drizzle olive oil over the chicken and place it on the grill. Cook for about 6-7 minutes on each side, or until the internal temperature reaches 165°F. Remove from the grill and let it rest for 5 minutes before slicing.
In a separate bowl, combine cream cheese, mozzarella cheese, cheddar cheese, basil, mayonnaise, and Dijon mustard. Mix until well combined.
Spread the cheese mixture evenly on one side of each slice of sourdough bread.
Layer the sliced grilled chicken on four of the bread slices, then top with the remaining slices, cheese side down.
In a large skillet, melt butter over medium heat. Place the sandwiches in the skillet and cook for about 3-4 minutes on each side, or until the bread is golden brown and the cheese is melted.
Remove from the skillet, slice in half, and serve warm.