Wasn't sure where to put this
Step 1. Log into Nexon.net
Step 2. Go to Charge Your Account and go to Earn Free NX
Step 3. Click the Peanut Labs section and then, just underneath the tab-banner type thing that says "Peanut Labs" right click.
Step 4. Click "View Page Source"
Step 5. CTRL+F and type in the letters "DOB"
Step 6. You will get your birthdate, however, it's not the full thing, only the year is correct.
Step 7. From here, you can manually input all 365 days and find your full birthday, if you really care about your account this much.
Note - I can vouch for this. This was used to recover my Elf's birthdate, the year given is indeed correct.
Credits to Swift of mabimods.net (Myself) and Limit of **********.net