| To sweat an onion is to cook chopped or diced pieces slowly in a small amount of butter or oil until they release some of their moisture and become slightly translucent. Adding a small amount of salt during cooking will draw the moisture out more rapidly. Depending on the quantity, you may want to cover the pan with a lid, but stir frequently and monitor the heat so that the onion doesn't begin to caramelize (turn brown).
Note: Grapeseed oil, olive oil, or butter are particularly good for sweating onions. But if you use butter, you may want to combine it with a little oil as butter burns at a lower temperature than oil.
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