In a small bowl, whisk the ingredients together until combined.
Place the mushrooms in a glass dish with marinade, and baste them with a pastry brush to properly cover them.
Place the grill pan on medium heat and oil it.
When the grill is hot, put the portobellos on that have been soaked in the marinade, cap side down. As they cook and you brush over them with the leftover fermented mixture occasionally, after 3-4 minutes you’ll start to see those beautiful grill marks formingon their caps.
Turn the eggs over and cook for another three minutes on each side. Remove from the grill pan and serve.