Clean mushrooms and add to the skillet. Season with salt and pepper. Let them brown and release some liquid. After about 5 min, add butter and thyme to the skillet. Cook until mushrooms are tender, about another 5 min or so. Transfer to a plate.
Wipe out pan and add butter on medium heat. Whisk 2 eggs and then pour into the pan. Let the eggs cover the whole bottom of the pan in an even layer. Let them sit for about a minute on low heat.
Add cooked mushrooms and goat cheese. Fold eggs on each side making a little package for the goat cheese to cook with the mushrooms.
Slice croissant and toast (or cook in a pan with some butter). Add eggs and drizzle with balsamic glaze. Enjoy!