When the butter has melted, add the shallots, thyme and garlic, and saute for a couple of minutes until the shallots have softened.
Add the mushrooms and cayenne pepper. Move the mushrooms around on the skillet to coat them with the spices. Cook for about 5 minutes, until the mushrooms have softened and have absorbed the flavors.
Add the balsamic vinegar and ½ cup of cream and stir to combine. Cook for about 1 minute, until the cream is infused with mushroom flavor. Season with salt if needed.
Add the mushroom mix into the four prepared ramekins. Crack an egg into each ramekin. Using the handle of a spoon, stir the bottom of the ramekin to mix the mushrooms with the egg whites (be careful not to break the egg yolks).
Boil some water in a kettle for the water bath. Place all the ramekins in a baking pan and transfer the pan into the oven. To create the water bath, carefully pour the water into the baking pan, about half way up the ramekins (making certain to not let the water inside the ramekins!).
Bake in the oven for 12 - 15 minutes, until the egg whites are set, but the yolk is still runny (the egg yolk will be very soft to the touch, but the dish will be set at the edges).
Remove from the oven, and then from the water bath. Sprinkle with salt and pepper and chopped parsley. Serve immediately with buttered toast.