Yes I think you are eligible. One purpose of OPT extension is to provide relief to those who are in their POST completion OPT but their H1B has not been granted yet.

Read  http://www.dhs.gov/xlibrary/assets/press_opt_ifr.pdf
and
http://www.murthy.com/nflash/nf_040908.html

One of the criteria for getting an OPT extension is that your employer should be enrolled in E-verification program (besides the obvious post-completion OPT status and STEM degree). Make sure that your employer participates in that (if it's not then you could request them to participate). The rest of the process is, I think, pretty similar to how you applied for your OPT. You will need to contact your DSO regarding that and he/she can tell you how to go about it. You should file for an extension before your OPT expires.
As for me, I am eligible in every other aspect besides my employer's participation in e-verification program. It's just too bureaucratic of a company and it takes more time than I have for them to make a decision about participating in the program. This clearly sucks and there's nothing more I can do besides go back to school or go back to Nepal. Well hopefully things will work out for you. Good Luck!

Yes civilnepali you can apply for the extension provided your company is E-Verified. You can request them and they will do it. I requested my Employer to register for it and they did, I am going to apply for the OPT Extension soon.

Remember, you must apply for the extension before your current OPT Expires.

Good Luck!!!

Junkiri try to find another employer!

hey civil nepali

e-verify thing is just simple and easy and is more benificial to the employers than to us. I talked to my employer and he did enroll on the same day. It's just that easy  but your employer should at least listen to you about e-verify. In my case I just printed  few sheets about e-verify from USCIS and gave them to my owner, he read it and was impressed about that and instantly told the Administrative staff to enroll. By the end of the day my employer was E-verified. So just tell your employer that it's good for the company itself,, i think they shouldn't have problem.

All the best