Preheat the oven to 400˚F.
In a medium sized skillet over medium-high heat, melt the butter. Sauté the finely chopped green garlic until fragrant, about 2-3 minutes. Add the mushrooms and cook until they have softened, about 3-5 minutes. Season with the salt and pepper. Divide the mixture between two oven-safe individual portion dishes placed on a baking tray. Using a large spoon, make two indents in the mixture in each dish. Break an egg into each indent. Divide the cream between the two dishes and transfer to the oven. Bake in the oven for 5-10 minutes, depending on how runny or cooked you like your yolks.
Once finished baking, sprinkle some more salt and/or pepper on top before serving if desired.
If you don’t own individual oven-safe dishes, you can use a small skillet. Cook the garlic and mushrooms in it and then break the eggs into the skillet and transfer to the oven or cover with foil and continue to cook on the stove.
If you cannot find green (new) garlic, you can substitute with spring onion.