The problem: The grocer only agrees to give a large bunch of cilantro (coriander) or mint leaves, and I need it to last a month or more, because I don't use the herbs as frequently. What I've tried earlier:  I've poured some water into the plastic bags containing the cilantro or mint, so that their roots (and leaves) were wet, and this was stored in the fridge. (turns out, wet leaves tend to rot faster)  I've blanched cilantro leaves, placed it in a plastic zip-lock bag and kept it in the freezer. When I took it out and let it thaw, it looked like greenish yellow seaweed, and a good amount of water had collected in the plastic bag. The cilantro didn't smell too good either.   What I'm asking about: I want to know if it's advisable to chop up fresh cilantro or mint leaves, boil some water or oil in a thick-bottomed container, and simmer the chopped cilantro or mint in it until it gets fully cooked. Then I could store it in the fridge or chill-tray (or if it's cooked in oil, I guess I could store it in the freezer). I'm hoping this would make it last longer and preserve the flavors too. One thing I'm worried about is, whether cooking it in this manner will make the cilantro taste bitter. When making mixed vegetables curry or chicken curry, whenever I've added cilantro before adding the chicken or vegetables, the curry ended up having a slightly bitter taste. ps: From this answer, I see I can store them in the freezer without blanching (but it needs to be kept within a paper towel). It is said to mess with the texture though. 
No, it is certainly not advisable. Cooking reduces the fridge life of plants. If you cook your herbs, they will only last 3 days in the fridge. Besides, you will also change the taste, and not for better. The advice you found on freezing is indeed the only way to keep herbs for a month. They do indeed look unappetizing when thawed, but you are supposed to use them in soups and other hot dishes, where the change in texture won't be noticeable. You should just throw them in without thawing, it is not only less work, but all that juice leaking out will go into the dish, instead of getting thrown out with the bag. If this does not work for you, the only other methods are to either switch to cooking with dried herbs (much more convenient, but very different taste) or to grow you own. But you cannot preserve the picked herbs in their fresh state by any method. 