You'll want to cook your grilled cheese in an oven (that's how we do it at the restaurant; you can use other methods, like a panini press or griddle of course). For best results, preheat your oven to 500 degrees F, and while preheating, make sure your cooking surface (sheet pan or tray) is inside the oven, so it's already hot when you plant the "raw" assembled sandwich on it.
Preheat the oven to 500 degrees F.
Spread a thin layer of salted butter on the outside of each piece of sourdough bread. Place a single layer of cheddar on the inside of the sourdough bread. Be sure to cover the full inside of the bread. Place a single layer of havarti on top of the cheddar, and be sure to cover the layer of cheddar. Place a single layer of Monterey jack on top of the havarti, and be sure to cover the layer of havarti. Place the other piece of buttered bread (butter-side out) on top of the Monterey jack to close the sandwich.
Carefully, place the sandwich on the hot sheet pan or tray. Place the sheet pan or tray into the heated oven. Cook for 45 to 60 seconds, until the top slice of bread achieves golden-brown toasting.
Remove the sheet pan with sandwich and flip the sandwich. Place the sheet pan back in the oven. Cook for another 30 to 34 seconds, until the top slice of bread achieves golden-brown toasting and all cheese is fully melted.