In Japanese used in newspapers or magazines, this behavior is written as
or
in Hiragana, and we seldom see
it expressed as 
.
The reason why is that this character is not designated for everyday
use.
What behavior does the phrase "make a pot of tea" describe? When you say "Here is a tasty soft adzuki-bean jelly, let make a pot of tea", then you are expected to pour tea from a teapot into a teacup. However, the behavior of making a pot of tea does not make you feel comfortable. There is likely another intended nuance aside from the effort to pour tea into a teacup.
You are expected to follow a series of steps:
1. Bring water to a boil.
2. Put tea leaves in the teapot.
3. Pour hot water into the teapot.
4. Pour the brewed tea from the teapot into teacups.
5. Place the teacups on a tray and serve teas to your guest or guests.
The expression
(make a pot of tea)
implies several simple steps, including boiling water and pouring tea
into teacups. Meanwhile, making a cup of
tea should reasonably include a series of steps to make
a drink such as a cup of tea and could be seen not to normally include the action of actually
pouring the tea into a teacup.
Specifically, making a cup of tea entails the actions of dipping tea leaves in a teapot filled with hot water and brewing the tea, which extracts the flavor and resonance from the tea leaves themselves.
This effort is specifically expressed by the kanji character
. 
is a meaningful kanji to express such actions as leaching substances
(such as tea) in a vessel or dipping tea leaves in water. Therefore,
using this Kanji allows you to depict the behavior of making a cup
of tea.
It takes time until tea leaves soften in the teapot and the extract of tea is obtained. In other words, the best advice for making tasty tea is simply to be patient. We want the
(brew) to bring to mind
the "anticipation of tasty tea"
.
