Two of my 10mm screws for the sparkplug cover have broken heads. The screws are sticking out is in place. What is the best way of removing it?

 

Not trying to be critical--but, you ought to bring it to someone else to get it fixed. Your mechanic has the rt tools. No reason those bolts ( not screws) were that tight.

 

Grasp the screw shank with locking pliers and slowly turn it counterclockwise until it’s free.

Since you have some thread left. vice grip and lots of WD-40 on the thread.
I would suggest removing the black plactic cover before the vice grips marr it up.

 

Yeah, I didn't notice it when I bought the car or I would have made the dealer take care of this.

 

One of the screw has the thread sticking out which I can probably use locking pliers. The other one doesn't so not sure what to do. Google said to get screw remover drill bits, drill it in to the broken screw and hand twist counterwise to remove. Does sound right?

 

Easy Out
Sears has them in stock where I live.

 

+1 on the easy out. Just be careful you can do more damage. A far fetched idea is to tack weld another bolt onto it with just a spot weld and use the head of that bolt to remove the bad one

 

loads of ways to deal with it, ive had my best success with my Snap On left handed drill bits and extractors

 

Does your avatar say AMOG?
Go to the sheet metal shop and give them a 6 pack.

 

+2. Bought this just last week.