Warm the skillet over high heat. Add one Tbsp olive oil to pan.
Spread the butter onto the bread - distributing evenly between two slices. Place the buttered bread - butter side down - in the skillet. Allow to cook for a minute or two while you tear the cheese slices.
Flip the bread, buttered side up and add the cheese to one slice of bread. You can remove the second slice for now - out of the pan.
Turn the heat to low and carefully add 1-2 ice cubes to the pan - immediately covering the pan with either a lid or foil so that the trapped heat and steam melts the cheese. Let the steam do it's magic for a minute, then turn the heat back to high. Tip: If needed, repeat with another ice cube. The ice will gently moisten the bread, but this actually works nicely! Your best bet is to use a hearty bakery bread that is about a day old.
With your heat on high and the cheese melted, add the fresh basil over top the cheese. Add a tiny sprinkle of the Italian herbs too. Then cover the cheese buttered side down with that slice of bread you set aside.
Drizzle another tablespoon of olive oil over top the sandwich - soaking the bread. Then flip the sandwich. The bottom side should be nice and toasty by now.
Cook for another minute or two to toast the bread on the bottom side. If needed, you can press the sandwich down with a spatula or heavy lid to speed to toasting process and further mash the flavors together.
Last step! Sprinkle another pinch of Italian herbs right over top the sandwich. Then flip. Add another pinch of herbs to the other side. cook another minute then remove from pan. Tip: For extra decadence and toasty edges you can add a bit more oil to the bread before flipping that last time.
Slice and serve warm!