Omelette with asparagus

Based on this recipe from Cooks Illustrated (subscription required). Helpful video is also at this link.
Serves 2.  

INGREDIENTS

3-4 stalks asparagus (8-10 thin asparagus, preferred)
small onion
4-5 mushrooms
1 clove garlic
4 eggs
3/4 cup finely grated Gruyere
2 Tbl butter
salt
pepper
vegetable oil
lemon juice (optional)


PREPARATION

1. Mince the onion and set aside.
2. De-stem and chop the mushrooms. Set aside.
3. Mince the garlic and set aside.
4. Chop the asparagus into 1/2" pieces. Set aside.

5. Heat oil in nonstick skillet on medium high and saute the mushrooms.

6. After 2-3 minutes, add onion and continue sauteeing.

7. After another 2 minutes or so, just before the onions begin to brown, add the garlic.

8. Sautee for another 30 secs or until fragrant, place sauteed mixture into bowl and set aside.

9. Melt 1 Tbl butter in the same skillet on medium high and when butter is foamy, add chopped asparagus.

10. Sprinkle with salt and stir asparagus occasionally for 3-4 minutes, until bright green and mostly cooked but not entirely. (For very thin asparagus, cook only 1-2 minutes).  

11. As asparagus cooks, in a medium bowl, mix the eggs with some salt and pepper.

12. Put asparagus in bowl, squirt a bit of lemon juice (optional), toss, and set aside.

13. Melt another Tbl of butter in the same skillet on medium low, and when butter is foamy, add the eggs.  

14.  Cook, without stirring, until eggs begin to set, 45 seconds to 1 minute. 

15. Using rubber spatula, lift edge of cooked egg, then tilt pan to one side so that uncooked egg runs underneath. 

16. Repeat process, working around pan edge. If necessary, use spatula to guide uncooked egg gently toward rim of skillet, until top is just slightly wet. Entire process should take 1 1/2 to 2 minutes. 

17.  Let pan sit on heat without moving for 30 seconds. 

18. Remove pan from heat, sprinkle asparagus and mushroom mixture in even layer over omelet, then sprinkle cheese evenly over asparagus. 

19. Cover and let stand so the eggs and veggies will continue to cook, 4 to 5 minutes.

20. Cook again for only 30 seconds on medium to finish, then either slide omelette halfway onto plate and use skillet's edge to flip the remaining omelette on top; or slide whole omelette onto plate and use spatula to fold.