Preheat oven to 375. Brush a 9'''' x 9'''' baking dish with the oil.
2
Cut the asparagus into 1/2in pieces and slice the mushrooms. Put the asparagus and mushrooms in the baking dish. In a medium bowl, whisk the eggs with the oil, mustard, Italian seasoning, garlic powder, salt, and pepper. Pour over the vegetables. Use a fork to distribute the vegetables evenly in the egg mixture.
3
Bake for 25 to 30 minutes, or until knife inserted near the center comes out clean. The quiche will puff up while baking and deflate when removed from the oven. Let cool for 5 to 10 minutes before cutting and serving.