Preparation Combine 1 cup water and sugar in medium saucepan. Stir over medium-high heat until sugar dissolves and mixture comes to boil. Reduce heat and simmer 5 minutes. Transfer to bowl and chill until cold. Puree quartered strawberries in processor until smooth. Add lime juice and sugar syrup; process until blended. Chill mixture until cold, about 1 hour. Transfer strawberry mixture to ice cream maker and process according to manufacturer's instructions. Spoon sorbet into container; cover and freeze until firm, about 4 hours. DO AHEAD Can be made 3 days ahead. Keep frozen. Scoop sorbet into individual glasses or bowls; garnish with strawberries. Serve Shortbread Cookies alongside.
Preparation Combine 1 cup water and sugar in medium saucepan. Stir over medium-high heat until sugar dissolves and mixture comes to boil. Reduce heat and simmer 5 minutes. Transfer to bowl and chill until cold. Puree quartered strawberries in processor until smooth. Add lime juice and sugar syrup; process until blended. Chill mixture until cold, about 1 hour. Transfer strawberry mixture to ice cream maker and process according to manufacturer's instructions. Spoon sorbet into container; cover and freeze until firm, about 4 hours. DO AHEAD Can be made 3 days ahead. Keep frozen. Scoop sorbet into individual glasses or bowls; garnish with strawberries. Serve Shortbread Cookies alongside.