Heat a cast iron pan over medium heat and melt 2 tbsp butter with 1 tbsp olive oil.
When the butter melts and beings to sizzle, place two slices of sourdough and wiggle around in the pan to coat evenly.
On top of one slice of bread, place 2 slices of white American cheese and 2 slices of pepper jack.
Place the other slice of bread on top and press down with a spatula or sandwich press.
While sandwich is cooking, grate over an even amount of fresh parmesan and when it melts, flip sandwich over and grate another layer of parmesan over the other side.
Once cheese melts on second side, flip and cook for 3-4 minutes to crisp.
Cheese should be melted and crispy around the edges of the bread.
Transfer grilled cheese to a plate and top with sea salt and fresh lemon juice.