Grate cheddar and Gruyère cheeses into a bowl; soften the butter and mix with oregano, garlic powder, parsley, and sea salt.
Slice Hawaiian rolls horizontally, keeping them hinged. Spread seasoned butter on both cut sides.
Layer with American cheese (if using), then sprinkle grated cheddar and Gruyère over the bottom half. Press the top back on and spread remaining butter on top.
Heat a skillet over medium-low heat; place the assembled roll block butter-side down. Cook for 5-7 minutes until golden brown.
Spread remaining butter on top; flip carefully and cook another 5-7 minutes until both sides are crispy and cheese melts.
Let rest before slicing into mini sandwiches and serve warm.