"Mijn broers hebben daar gegeten."
Translation:My brothers have eaten there.
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.