most people think of a gimlet as a drink with gin, but actually there are gimlets with vodka as well. mine comes not only with lime but limoncello as well:
limoncello basil gimlet
limoncello is an italian lemon liqueur which has a very distinct lemon flavour, if drinken pure it always used to remind me of washing up liquid (due to the smell and colour, as it is bright yellow), but in cocktails it develops a nice lemon taste!
mix 3 parts of vodka, 2 parts of limoncello and 1 part of freshly squeezed lime or lemon juice in a cocktail shaker and add three leaves of fresh basil. shake well with a couple of ice cubes and strain into a martini glass. add the broken up basil leaves from the shaker to the drink as well. the basil only gives a ‘green and herby’ hint to the gimlet and mixes well with the lemon flavour!