A short cooking time (under 7 minutes) is a must to keep green vegetables bright green. Lenth of cooking time is important to the taste of many vegetables, too. Onions become milder and sweeter with longer cooking times. Roasted onion halves whose cut surfaces are well-browned become deliciously sweet. Onions browned on a grill are a sweet complement to any meat.
Members of the genus brassica (cabbage, cauliflower, broccoli, Brussel sprouts, kale, mustard, rutabagas, collards, turnips, etc.) become stronger and more unpleasant the longer you cook them. Even 2 to 3 minutes additional cooking time matters. The amount of strong-smelling (the smell of rotten eggs) hydrogen sulfide gas that comes off of cabbage doubles when you cook it 7 minutes instead of 5. Cabbage that is slivered fine (as for slaw) can be cooked in a few minutes. Serve with buttered bread crumbs or herbs, it is sweet and mild. You will notice a major change in sweetness and mildness of these vegetables if you come up with creative ways to cut them into small pieces that will cook in a short time.
When you cook green vegetables over 7 minutes, their chlorophyll loses its magnesium and they turn yucky army-drab green. Acids also cause this same loss of magnesium and the resulting army-drab green. This is why beautiful snow peas and broccoli in a pasta primavera turn brownish. Always stir dressings containing vinegar or lemon juice on green vegetables just before serving. Or, avoid vinegar and lemon juice altogether and use lemon zest (grated peel) for zippy flavor.