Most tea drinkers have very good ideas about what can cause over-brewing of a green tea. What I want to discuss here is a series of factors that may cause over-brewing, in a sequence of their significance as far as I can see.
2. Volume of water
4. Infusion time
5. Leaf/water ratio
This discussion is out of the thought that some factors are more likely to cause over-brewing, but are often neglected (for example, steaming factor). On the other hands, some other factors are not as likely to cause over-brewing, but are sometimes over-emphasized (for example, temperature factor).
Before I start, I would like to stress that tea brewing is a very personal matter, and there can always be a lot of variations in methods and brewing parameters. Eventually what works is the best, and different ways may work for different people. Sometimes we break some rules, not to prove these rules are wrong, but to demonstrate it's wrong to rule out other possibilities.
Brewing tea is a process of extracting good flavors out of tea leaves into the tea liquor. Here I will define "over brewing" as brewing that causes unpleasant flavors to be extracted or generated - this is what people say a tea is "cooked". "Under brewing", in my understanding, is brewing that fails to extract most good flavors from tea leaves.
I usually suggest people to use un-lidded vessels for green tea. Traditionally, gaiwan was a very popular vessel for green tea. But when gaiwan was used to brew green tea with young and tender leaves, the lid was either not placed or only used to cover the cup half way.
People with cooking experience may have noticed this. When you saute some green vegetables in a pan on the stove top, as long as you carefully control the process, you can make the sauteed veggies juicy, tender and crisp, with their nice green color. But if you leave the freshly sauteed vegetable in a sealed container or covered dish for several minutes, it can get pale and soft, losing half of the flavors. What "kills" the veggie dish is also what sometimes "kills" the green tea - steaming, not high temperature.
Why were teapots used in the traditional society for green tea then? I guess, it's because teapots (especially yixing) are good at retaining temperature. This could be important in the traditional society when the rooms were not well-heated in winter. When using teapots in the traditional society, people were struggling with cold environment, and were not worried about over-brewing due to hot environment. This is also why gaiwan is a versatile tea ware. By placing the lid, placing it half way or removing it, you can adjust the brewing environment in the cup.
It's not that a lidded vessel is less good for Chinese green tea. And I personally have a favorite yixing reserved for green tea. A tea drinker can adjust the temperature, leaf/water ratio and infusion time to make a lidded vessel serve very well. Naturally, when a lidded vessel is used, water temperature should be lower, in order to avoid the "steaming" effect. But then the "catch" is, when lower water temperature is used, there is the risk of "under brewing", which will be elaborated in the third section about Temperature.
2. Volume of water
When you use a small gaiwan (4 oz. of less) for Chinese green tea, as long as it's not fully lidded and steamed, feel free to use the hottest water, and the leaves will not be over-brewed. Of course, by adjusting the temperature a little bit, we can get better result. But when the volume is small, the danger of significant over-brewing is tiny or none. The wide opening of the gaiwan cup will allow steam to escape fast and temperature drop fast. This is just an experiment. I am not suggesting everybody to use a vessel as small as 4 oz. for green tea. (Besides, it could be hard for people with big hands!) A "small vessel" is probably something smaller than 180 ml (6oz.). But with a vessel up to 300ml (10 oz.) and with care, the vessel can release steam and lose heat fast, so that the tea will not be over-brewed.
Temperature and Heat are two different concepts. Think of the flame of match stick (temperature around 400 F) and a liter of hot water (temperature: 200 F). The flame has higher temperature, but with its small mass, it has by far less heat than the big pot of hot water. In tea brewing, it is the extra heat, not temperature, that over-brews a tea.
Some people may say, how inconvenient it is to use a tiny small vessel for tea! What if I want more! Well, first of all, I think we should be aware that in modern days, all our vessels, whether for tea, coffee, or many other things, have grown amazingly big. Many of them are so much bigger than what they used to be just a few decades ago. What's small to many of us today, was just normal size in the past. Believe it or not, when you have your tea, snack or other things in a small portion, it tastes better :-D Besides, you can always have multiple cups, with each cup carefully prepared and delicious. When large volume is used, then there should be caution about over-brewing, and other brewing parameters may need to be adjusted accordingly.
3 hours ago