I’ve had Coquilles St Jacques with cheese as often as I’ve had it without. I really liked a Peruvian Coquilles St Jacques that was topped with Parmesan. Might be more of a South American variation, but I liked it. I’ve also made this version with gruyere.
I often do a quick variation on Rockefeller with spinach and Parmesan. https://www.seriouseats.com/oysters-florentine-recipe
I’ve had something like this at Morro Bay. Quite simple. https://www.pacificseafood.com/recipes/parmesan-crusted-charbroiled-oysters/