So, if the verb starts with a vowel, we put an extra 'g' between 'ge' and the verb, correct? In this example, instead of "geeten", we say "gegeten".
No, with the regular past participles only the ge also with vowels including the e. For example geënterd. (Note the dots on the second e to mark the beginning of the new syllable otherwise one might mispronounce it with a long ee ).
Eten is irregular. I can't think of other examples so I wouldn't worry too much about it and just remember it's there in gegeten.
Oh I see, thank you! Anywhere to find these irregular verbs which don't take -t or -d at the end, but used with the original version of the verb (that is with -en in the end)?