Heat a large cast iron pan or another frying pan medium-low heat. As the pan heats, spread butter on one side of each slice of sourdough bread.
Place the buttered side of bread down in the heated skillet. Place a slice of cheddar and Swiss cheese on each slice of bread in the pan, allowing the cheese slices to overlap each other and end just around the border of the bread. Then cover the cheese with another slice of bread, this time, buttered side up.
Let it cook for 2 to 4 minutes on one side still on medium-low heat until golden brown then flip to the other side and let it cook for another 2-4 minutes until the cheese is melted and the other side is golden brown too. Repeat the process with the rest of the bread slices.
Remove the sourdough grilled cheese sandwiches from the frying pan, cut them in halves and serve warm.
Notes
Optimal Heat: Be sure to maintain the heat on medium-low to allow time for the cheese to melt without the bread burning.
Keeping Warm: If you make the sandwiches way ahead of serving time, set your oven to 200 to 250 degrees F then place the sandwiches on a baking sheet and keep them in the oven to stay warm. Grilled cheese sandwiches are best served warm so the cheese is enjoyed while still melted.