Combine water and sugar in a saucepan over medium-high heat; stir until sugar is dissolved. Mix strawberries into saucepan and bring to a boil; boil for 5-6 minutes. Reduce heat to medium-low and simmer until strawberries are mushy and sauce is thick, about 10 minutes. Cool and strain into milkshake glasses (refrigerate any leftover syrup). Transfer glasses (with the syrup) to the freezer while you prepare milkshakes.