Wipe mushrooms clean; then slice.
Heat butter in a non-stick skillet.
Sauté mushrooms for about 5 minutes.
Add thyme leaves and cook 1 minute longer.
Beat eggs and stir in Parmesan cheese.
Pour over mushrooms in skillet.
Cover and cook over medium heat until eggs are almost set.
Sprinkle with gruyere cheese.
Wrap handle or skillet with aluminum foil to heatproof.
Broil until cheese melts, about 1 to 2 minutes.
Remove to serving plate and cut into wedges.