I am looking through some recipes that came with a French pressure cooker I just bought (in Belgium). It seems most of the recipes that use garlic ask for one or two upeeled garlic cloves (ongeschilde teentjes knoflook). Is this really a thing, or am I misunderstanding something? If you include unpeeled garlic cloves, do you still chop off the end that used to connect to the heart?
Unpeeled onions and garlic help thicken liquids (just a little). The skins of onions and garlic are at least 10% pectin, the substance that is used to thicken jellies. If you are making a stock or a soup, you can place the washed unpeeled garlic or onion quarters in an oversized herb sachet. After cooking you remove the sachet and discard its contents.
The skins have also been found to be rich in antioxidants. You can read all about the science of garlic and onions in Garlic and Other Alliums. While it does discuss the antioxidant effects of Alliums in general it does not treat the particular compounds that have been discovered in the skins.
According to Trash Backwards, leaving skins on garlic in a roast allows the garlic to cook more evenly. There are multiple suggestions out there that say that the skins add additional flavor and nutrients to a broth.
It actually makes sense if preparing a broth or stock: you don't want the skin to come out while cooking and float in the stock: it won't be pleasant to see nor to eat.
On the other side, when roasting or sautéing, leaving the skin on helps avoiding the cloves burn, which would give an unpleasant taste.