Image from fooding
Sweating your veggies is easy: simply put your prepped vegetables in a pot on low heat. Keep the lid on, and let them cook slowly. By keeping the lid on, you use their own liquid to "sweat" (aka steam) them. The technique is called à l'étouffée in French cooking, and it leads to soups and bisques with depth of flavour.
You can also apply this to purees that are part of other dishes -- like mashed potatoes, for example. If you find yourself with leftovers, just freeze your soup or your puree for future use. For more better soup tips, check out the full post linked below.
7 Ways to Make Your Soups Even Better [Bon Appetit]