Midori Sour for green Long Island Iced Tea for brown (though that might be a bit strong for a signature drink). Mabye just an iced tea with some sort of alcohol mixed in?
I like the grasshopper idea, that way you can include both colors! The drink itself is minty and green, and you could have them put chocolate shavings on top or a chocolate stir stick - yup, I think mint & chocolate is the way to go for the ultimate brown and green combo!!!
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Re: Signature Drink
green - apple martini
Long Island Iced Tea for brown (though that might be a bit strong for a signature drink). Mabye just an iced tea with some sort of alcohol mixed in?