shabbat - Significance of the various Shabbos dishes

Many people (especialy chassidim) are very particular to have certain foods on Shabbos. Fish, soup, cholent, liver, eggs and onions, kugel, and I'm sure I'm missing a few others.

What is/are the significance of these foods? (asides from tasting good!)

What other special Shabbos foods am I missing?

Answer

I know a few but far from all - what I find interesting is that there are many halachic reasons behind them

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  cholent (from the French chaud-lent, hot-slow): can stay on the fire/plata all night therefore no issue with the melacha of hazara (returning a dish to be cooked)

  
  


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  gefilte fish: doesn't have bones so no risk to perform the melacha of borer (selecting the bad from the good)

  
  


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  kugel: possibly because it is dry and tastes good even without sauce, therefore no issue of bishul of a dish in sauce

  
  


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  fish in general: fish is the only animal that didn't fault before the mabul (flood) and therefore wasn't destroyed, see also here on MY

  
  


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  challot: two loaves of bread for lehem mishne (either the double portion of manna on Fridays, or shamor v'zakhor et yom hashabat)

  
  


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  couscous: I need a placeholder for this (my Sephardic wife wouldn't forgive me otherwise) but cannot think about the halachic background

  
  

As @Daniel notes in the comments, it is a mitzva to eat hot food on shabbos lunch, based on the words of Ba’al HaMaor (R Zerachiah HaLevi from Gerona, who lived in the mid-1100s) - from here

It is a Takanas Chachamim to enjoy the Shabbos with a hot dish. Whoever does not do so is suspect of being a ‘Min’ (heretic), the reason being that the heterodox Karaites, who denied the Rabbinic Mesorah, prohibited eating any hot food on Shabbos. The Ba’al HaMaor explains that one who refuses to eat a hot dish on Shabbos (cooked before Shabbos), is suspect of following their heretical interpretation of the Torah and not those of our Chachmei HaDoros.

Finally meat is not included in the list above, because, unlike what most people think, it is only a mitzva to eat meat if one enjoys it. Says the Mishna Brura 242:1 "[...] one should delight in Shabbat according to the custom, with food and drink that is considered delight for them. And since in general, most people get their delight from meat and wine and sweets, therefore [...] one should have a lot of meat and wine and sweets according to one’s abilities"