Place sundried tomatoes in medium-size bowl, add warm water and set aside.
Heat coconut oil in large, oven-proof skillet. Add onion and mushrooms and sauté until onions are translucent. Add garlic and asparagus and sauté for another 3 minutes. Transfer vegetables into a bowl and set aside.
In a large bowl, beat the eggs. Heat coconut oil in the skillet over medium heat, then add the eggs. Add the vegetable mixture, spreading it evenly through the eggs. Drain the sundried tomatoes and add those to the egg mixture. Sprinkle parsley over the top. Add salt and pepper as desired.
Turn heat to low and allow the egg mixture to cook until the bottom is set (15-18 minutes). Transfer the skillet into the preheated oven and allow the top to finish cooking (2-3 minutes).