杯
bēi
You're counting the cup, not the drink: 杯
The picture One cup held in your hand. Whatever fills it, what you count is the cup.
Where the picture shows up in 杯
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one at the café
我要一杯美式咖啡。
wǒ yào yì bēi měishì kāfēi
One americano, please.
In a bottle it's 瓶; in a bowl it's 碗. Change the vessel and you change the counter.
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one you ask for
请给我一杯热水。
qǐng gěi wǒ yì bēi rè shuǐ
Could I have a cup of hot water?
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two more you order
我们再来两杯啤酒。
wǒmen zài lái liǎng bēi píjiǔ
Two more beers, please.
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the one you adjust
这杯奶茶少放点糖。
zhè bēi nǎichá shǎo fàng diǎn táng
Less sugar in this milk tea, please.