This is an extremely decadent mid-afternoon meal, and the simplicity of the ingredients highlights the fresh, fresh eggs. A gratin dish is called for to bake this, which is an oval-shaped, shallow dish. If you don't have one, just use any small, shallow baking dish (or even an oven-safe bowl or mug.)
Turn on the oven to 350. Crack all four eggs into a small bowl, being careful not to break the yolks. If you have small gratin dishes, do two and two.
Add the bread crumbs, the chopped herbs and the cheese together in another bowl and loosely mix.
In a saucepan on the stove top, heat up the cream, the wine/vermouth and the butter over low heat, for 5 or so minutes until simmering (but make sure it doesn't come to a boil.) Meanwhile, place the gratin dish(es) on a cookie sheet and heat in oven a few minutes.
Remove the gratin dishes from oven, and pour in the cream mixture. Then carefully slide in the eggs, and top with a heavy handful of the cheese-bread-herb mixture.
Bake for 8 minutes, and then turn on broiler to high for 3 minutes. Check to make sure whites are set, but yolks still look golden (runny.) Serve with black pepper, and black tea with lemon.