Preheat oven to 300 degrees.
Sauté mushrooms and onions in melted butter for about five minutes. Add tarragon and remove from heat.
In separate bowl, beat eggs to make them fluffy. Add parmesan, salt, and pepper. Stir.
Lightly grease ramekins with seasoned/melted butter from the skillet you used to cook mushrooms.
Spoon mushrooms into bottom of ramekins. Pour in eggs.
Bake approximately 20 minutes. (If you want to create a design on top from onion, mushrooms, carrots, or other veggies, do that about 10 minutes into baking time.)
After the 20 minute baking time, cook an additional 5 minutes on broil. Keep an eye on it as oven times vary!