When should I have the pot covered uncovered, or ajar?

Less coverage = more evaporation=more concentrated flavor. Keep the pot covered if you want the ingredients to meld, cook and warm without reducing the amount of liquid. When the precise amount of water matters like when making rice- you’ll also want to keep that top on tight. The grains have to absorb every last drop On the flipside if you’re looking to deepen or strengthen flavors or to introduce new textures, as in a braise, open the lid.
Useful advice
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Thank you.
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