Start by making your basil simple syrup. In a saucepan, add the basil leaves, sugar and water. Heat over medium heat and stir while bringing it to a simmer, never to a boil. Continue for another 5 minutes. When it's ready, sieve it and transfer it to an airtight container.

In a cocktail shaker, add the ice, freshly squeezed lemon juice, basil syrup and vodka. Mix well until the shaker will become cold in your hands.

In a chilled martini glass, use a slice of lemon to create a rim of juice around the glass and then dip in sugar to create your sugar rim. Pour your basil lemon martini inside, garnish with a slice of lemon or basil leaf and enjoy!