I have a Master's in a non-STEM degree, but a Bachelor's in a STEM degree. I have already used my Master's F-1 OPT (12 months) and it will expire in June. I am wondering if I can still apply for the F-1 OPT STEM extension using my Bachelor's degree instead?
The rules for STEM OPT changed in May 2016, a year after you posted this question. Under the new rules, yes, if you are currently on OPT, you can apply for an OPT STEM extension on the basis of an earlier STEM degree, if it meets certain criteria. (In particular, you must have completed it in the US within the last 10 years.) Here is more information from Homeland Security about OPT STEM extensions.