Green tea is not to everyone's taste. You can try adding honey instead of sugar. As honey has more of a distinct flavour than just sugar it may help mask the green tea flavour more successfully. Another suggestion is to add some mint leaves if you're a fan of mint. If you're drinking green tea solely for health reasons the mint can be excellent for aiding digestion.
Certain tea companies also sell 'light' green tea. This can be more palatable, especially for people like yourself who don't like the taste of steeped green tea so changing your brand of tea might be helpful.
It may be that with perseverance you may acquire a taste for green tea (I personally used to hate camomile tea but continued to drink it every day and now it's my favourite).
Hmmm.....
Well, I've lived in India for 12 yrs & this is how I make 'masala chai' or 'spiced milk tea' at home & in my restaurant-
2 cups water
1 teaspoon black tea, loose leaf (I use Tokla tea from Nepal)
1 tablespoon grated fresh ginger
10 black peppercorns, coarsely ground
500 ml full fat 'whole' milk
Sugar to taste
In a stainless steel 3L pot combine tea, water, ginger & black pepper, bring to boil over high heat. Allow to boil for about 2 minutes.
Add milk to boiling tea, again allow to come to a boil. (Watch the pot closely in case the milk begins to foam, if it does foam- stir & decrease heat a little) Allow to simmer uncovered for 6 minutes.
Remove from heat, let stand for 2 minutes. Add sugar to taste if desired & stir. Use a tea strainer to strain into cups to serve. (or serve sugar on the side so people can add sugar to their own tastes)
Some notes-
I think you are trying to make 'tulsi' chai?
Tulsi = Indian holy basil
If so usually the fresh tulsi leaves (around 8-10) are added to the boiling tea mixture with around 8 green cardamoms, 2 cloves, 1/4 tsp fennel seeds, and a pinch of cumin seeds as I recall. Some Indians dry roast the whole spices to mellow the flavor a bit.
Use spices like fennel, cloves, star anise, cumin sparingly as their strong flavors can take over & give the chai a 'mouthwash' taste which isn't pleasant.
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The most likely culprits are:
Here is an excellent resource for getting these factors right:
On Steeping Time:
On Temperature
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Read the whole thing for further background.