Egg week - day 3 (herb-baked eggs)

What I must do here is give Ina Garten her due. This started as essentially her recipe, although my notes say “adapted from”. It doesn't matter, does it Ina? Between the two of us we have a very special breakfast or brunch dish. I think I could manage 6 of these at one time, but I cook for two nearly all the time. Ergo, here's a recipe for two. Serve this with toast or, if you are ambitious, make some biscuits.
Herbed-baked eggs
1/4 teaspoon minced fresh garlic 1/4 teaspoon minced fresh thyme leaves 1/4 teaspoon minced fresh rosemary leaves 1 tablespoon minced fresh parsley 1 tablespoon freshly grated Parmesan 6 extra-large eggs 2 tablespoons heavy cream 1 tablespoon unsalted butter Kosher salt Freshly ground black pepper
Preheat the broiler for 5 minutes and place the oven rack 6 inches below the heat.
Combine the garlic, thyme, rosemary, parsley, and Parmesan and set aside. Carefully crack 3 eggs into each of 2 small bowls or teacups (you won't be baking them in these) without breaking the yolks. (It's very important to have all the eggs ready to go before you start cooking.)
Place 2 individual gratin dishes on a baking sheet. Place 1 tablespoon of cream and 1/2 tablespoon of butter in each dish and place under the broiler for about 3 minutes, until hot and bubbly. Quickly, but carefully, pour 3 eggs into each gratin dish and sprinkle evenly with the herb mixture, and then sprinkle liberally with salt and pepper. Place back under the broiler for 5 to 6 minutes, until the whites of the eggs are almost cooked. (Rotate the baking sheet once if they aren't cooking evenly.) The eggs will continue to cook after you take them out of the oven. Allow to set for 60 seconds and serve