If you're like most of us, you don't give this much thought. If you're in a hurry...you turn up the heat. But this fabulous video lesson from Rouxbe will change your mind.
Bottom line...boiling draws out moisture. So it's best to simmer or poach meat and chicken. The results, while taking a few minutes longer will result in juicier meat. Ever wonder why sometimes your chicken from your chicken soup is rubbery? Chances are it's because you let the water boil, thinking it will absorb more nutrients and flavor into the broth. Remember that slower, is better.
But not everything should be simmered...pasta needs boiling water from the start, and according to Jamie Oliver, potatoes do best when dropped into boiling water too. Rice, on the other hand gets put into a pot of cold water, brought to a boil, and then reduced to low (simmer) to absorb the water and make the rice tender without turning to mush.