Preheat the oven to 375°F (190°C).
Pour half a cup or more of heavy cream into a shallow earthen dish or ramekins, enough to cover the bottom of the dish.
Place the dish or ramekins in a larger pan filled with boiling water, creating a water bath.
Once the cream is hot, break as many eggs as the bottom of the dish will hold, being careful not to break the yolks.
Cook the eggs in the hot cream until they are well set, basting them occasionally over the top with the hot cream.
Season the eggs with salt and pepper to taste.
Serve the creamy baked eggs promptly.