I'm having trouble finding a particular historical reference.
In On Manly Courage: A Study of Plato's Laches, on page 57, the author implies that Spartan common meals were followed by the recounting of noble deeds. "[Lysimachus] and Melesias are raising their sons in the bracing military discipline of the Spartan syssitia (common meals), and evenings after dinner they tell the boys tales of their ancestors' noble deeds (kala erga) in war and peace." While he doesn't outright say it, in context it seems fairly clear that he means that recounting deeds after meals itself emulates a Spartan practice.
If this is the case, I'd like to confirm it with a primary source. If not, I'd like to confirm otherwise from someone more familiar with Spartan history.
Wikipedia seems to confirm the point, at least for Crete if not Sparta, saying meals were followed by "conversation, which was first directed to the public affairs of the state and afterwards turned on valiant deeds in war and the exploits of illustrious men, whose praises might animate the younger hearers to an honourable emulation." But it does not cite a clear source for that. Plutarch in his Life of Lycurgus says "They used to send their children to these tables as to schools of temperance… " Aristotle makes several references to common meals in Politics, but a word search did not turn up what I was looking for. I also looked at book four of Athenaeus, which is referenced on the above wiki page, but the Lacedaemonian section didn't have the answer.
Is there a primary source that confirms Spartan (or reasonably comparable, i.e. Cretan) common meals were followed by the recounting of public affairs and noble deeds?
Edit: As sempaiscuba rightly pointed out, the Wikipedia article is quoting Athenaeus after all (found here) - I'd just gone a little cross-eyed and went off looking in the wrong place. But this still refers to Crete of course. As stated above, that works just fine for my purposes, and it may very well be the passage the Laches commentary is obliquely referencing, but I'll leave the question open for another day or two in case anyone has an answer for Sparta in particular.
For Sparta, "great deeds" is mentioned by Xenophon (c. 431 to 354 BC) in Constitution of the Lacedaemonians where he relates this in the context of the young gaining part of their education from the experience of their elders:
Note that in other states the company usually consists of men of the same age, where modesty is apt to be conspicuous by its absence from the board. But Lycurgus introduced mixed companies at Sparta, so that the experience of the elders might contribute largely to the education of the juniors. In point of fact, by the custom of the country the conversation at the public meals turns on the great deeds wrought in the state, and so there is little room for insolence or drunken uproar, for unseemly conduct or indecent talk.
Plutarch (c. 46 to c. 120 AD), writing much later during the Roman period, also mentions discussions at public messes or phiditia or syssitia (known as andreia in Crete), in Lycurgus. However, he makes no reference to "noble deeds", though your phrase "recounting of public affairs" may well be covered at least in part by his reference to "political discussions":
Boys also used to come to these public messes, as if they were attending schools of sobriety; there they would listen to political discussions and see instructive models of liberal breeding.
A little further on in Lycurgus, Plutarch, in relating one part of the role of the Eiren (a man in his twenties in command of a troop) in the training of boys, mentions after-meal discussions:
The eiren, as he reclined after supper, would order one of the boys to sing a song, and to another would put a question requiring a careful and deliberate answer, as, for instance, "Who is the best man in the city?" or, "What thinkest thou of this man's conduct?" In this way the boys were accustomed to pass right judgements and interest themselves at the very outset in the conduct of the citizens.
This almost certainly took place in the mess (Xenophon, cited above, specifically mentions mixed ages) as the eiren, in turn, was being observed and assessed by his elders and all Spartan men were obligated attend their mess for meals.
Unfortunately, most of the literature which would probably have contained more information on messes has not survived. The works on constitutions of Sparta of both Critias (a pupil of Socrates) and Aristotle (one of Plutarch's sources) have only survived in fragments. Another potentially invaluable source, Sphaerus (c.285 to c.210 BC), a Stoic philosopher and advisor to King Cleomenes III has fared even worse; we know only the titles of his works Lacedaemonian Constitution and About Lycurgus and Socrates.
Hans van Wees, 'The Common Messes'. In Anton Powell (ed), 'A Companion to Sparta' (vol. 1, 2018)
This is too long for a comment, but is certainly not a complete answer. However, with that caveat, Athenaeus of Naucratis certainly wrote about that practice in the Cretan commons in his Deipnosophistae.
Quoting Dosiadas' 4th book on Cretan History, he says:
"… After dinner they are in the habit first of deliberating on public affairs; from that subject they proceed to call up deeds of prowess in war and to praise the men of proved bravery, in order to encourage the younger men in the pursuit of virtue."
- Athenaeus, IV, 143