In a medium saucepan, bring the strawberries, sugar, and water to a simmer on medium-high heat. Reduce heat to low and simmer 15-20 minutes until the syrup is thick and strawberries are very soft.
In a large, fine mesh sieve set over a bowl, strain the syrup, but do not press on the solids. Chill syrup until at least room temperature. Use for cocktails or refrigerate for up to five days.
To make a single drink:
Shake vodka, syrup, lemon juice, and a handful of ice in a cocktail shaker. Strain into small coupe glasses (or cocktail glasses of your choice).