Why do we serve Arbes - chickpeas at a Shalom Zachor?
Aveilus for the Torah forgotten. Taamei Haminhagim 902
Another explanation is it's a Yiddish/Hebrew pun, referencing to G-d's blessing to multiply Abraham's offspring: "arbeh es zar'acha".
Rabbi Joseph Dov Soloveichik's last public event (due to his declining health and mental function) was the wedding of Rabbi Kenneth Brander. Rabbi Brander told his ailing mentor, "G-d willing we'll have you for many more happy occasions, maybe soon we'll have a boy and we'll invite you to his Shalom Zachor." Rabbi Soloveichik replied, "don't serve chickpeas."
Rabbi Brander is uncertain whether the comment was one simply of "I don't think I'll make it", or if Rabbi Soloveichik genuinely felt that we shouldn't serve chickpeas. The case could be argued, he said, that we don't mourn forgetting the Torah, as now we earn it on our own instead of it being a freebee. (Corresponding to Rabbi Chaim Volozhiner's recording how his mentor, the Vilna Gaon, ordered his disciples to refuse any angel who might come and offer to teach the entire Torah -- we do it ourselves, thank you very much!)
My speculative, unresearched reason for this custom is that it's based on the Gemara and Shulchan Arukh's edict to eat foods which increase sperm on Friday night. In medieval times, it was believed that chickpeas was one such food.
Interestingly, based on the sources brought down in Mishna B'rura, we may also explain why the chickpeas are served with black pepper as opposed to salt.