Roughly chop the strawberries and place in a small saucepan with the lime juice and basil. Bring to a boil, then reduce heat to simmer. Cook until strawberries are softened, and use the back of a spoon or a potato masher to puree the strawberries. Remove from heat and allow to cool.

Once cool, place a fine mesh strainer over a bowl. Pour the strawberry puree into the strainer and use a rubber spatula to press the mixture through. This will strain out any seeds and the strips of basil.

Place ice in your shaker cup followed by the vodka and the puree. Shake until cold and mixed well.

Pour evenly into two martini glasses and garnish with strawberries and basil leaves, if desired.