Set oven to Broil, and let heat for about 5 minutes. Place rack no higher than 6 inches from the burner.
Take a shallow gratin dish, and place 1/2 tablespoon of butter and 1 tablespoon of heavy cream in the dish. Place in oven and heat until the cream and butter start bubbling, about 5 minutes.
Mix chopped herbs, garlic, and grated parmesan cheese together and set aside.
Crack 3 eggs carefully into a small bowl, taking care not to puncture the yolk.
Once the cream and butter are bubbling hot, remove the gratin dish from the oven and set on a trivet. Pour the eggs into the gratin dish and sprinkle with the herbed parmesan mixture until well covered. Sprinkle salt and pepper liberally all over.
Place gratin dish back in the oven and broil for about 5 minutes. The dish should be done when the edges of the gratin and the garlic from the herb mixture are nicely browned.
Remove from the oven and let sit for about 1-2 minutes, to cool and set the eggs.
Enjoy with a slice of baguette or your favorite bread.