Pour a layer of rock salt in a sheet pan to cover bottom. Shuck oysters and set on rock salt. Place in refrigerator while preparing remaining ingredients.

Place spinach on a sheet pan, drizzle with oil, and sprinkle with salt. Place in oven and cook until just wilted, about 1–2 minutes. Remove and set aside to cool. Thinly slice cheese into pieces small enough to fit on opened oysters. Top each oyster with a small amount of spinach followed by a slice of cheese. Sprinkle lightly with nutmeg. Cook in oven just until cheese is melted, about 2 minutes, and remove. Be careful not to cook the oyster. The cheese and spinach should be warm with a cold briny oyster beneath.