How can I improve rich taste of spiced milk tea?

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.

Be careful you aren't burning your milk for one. Milk needs low heat and constant motion to make sure that the fats don't settle at the bottom of the pan and get overheated.

You should also make sure your tea isn't oversteeped. Tea has a tannic flavor that can be overwhelming when allowed to boil for too long. To solve this, I'd recommend using an infuser. That way, when the pot of milk tea has reached the right level of tea flavor, you can remove the tea and continue adding spices or sugar and cooling the tea down until it's ready to serve.

Have you looked at recipes for other milk teas?

Traditional Indian chai is made by boiling the milk first and adding the tea and spices and allowing them to infuse in the milk and its fats. This gives it a bold, rich flavor that lingers on your tongue. The bitterness of cloves/ginger/cinnamon/cardamon is offset with adding the right amount of sugar of course. And I think any variety of black tea makes a good match, but assam is the traditional choice.

I'm aware that Indians have a kind of chai that is not a milk tea that's served with basil and lemon, a refreshing tea like a lemonade. Basil milk tea does not sound like a good match to me but I'd be curious whether removing basil alone would fix this issue.

English add cream or milk after the tea has been poured to offset the bitterness of it, for the same reason most Western Europeans/North Americans add milk to coffee. If there's any citrus in the tea, you'll have to use heavy cream to prevent it from curdling which is unsightly and will ruin the taste of the tea.

Lastly, for Asian milk teas, I've never actually had real milk used in the making of Bubbletea.

Black tea is best suited for milk tea as it is strong enough to make it's presence felt even with so much milk. If you use oolong/green tea, which has milder flavors, the taste of the tea will be overpowered by the milk and the sweetness of the sugar.

Also, you should consider letting the tea steep in the boiling water before adding the milk. As milk is a much denser liquid, tea takes much longer to infuse and you increase the risk of tannins getting released which might make the tea taste bitter. Refer to this chart for approximate tea steeping times.

This one is purely subjective, but basil seems like a strange herb to add to milk tea, I do not think it's flavor profile goes well with tea. In any case, most basil, when cooked, tend to become very bitter, so I would reconsider the spice/herb mixture you are using.