In a small saucepan over medium heat, combine water and sugar. Cook and stir until sugar dissolved. Remove from heat and cool for about 45 minutes.
Place the strawberries, 4 mint leaves and the lime juice in a blender or food processor. Blend until smooth. Add half of the cooled sugar syrup. Taste and adjust with more mint leaves and sugar syrup. Make sure the mixture is slightly sweeter than you want, because it will be less sweet once it is frozen.
Transfer the mixture to a flat-bottomed 9 x 13-inch baking or glass dish. Keep in the freezer and chill for 30 minutes.
Stir the mixture thoroughly with a fork and freeze again for 30 minutes. Continue to freeze for another 4 hours, scraping and breaking the mixture with a fork every 30 minutes. Scoop to serving cups and serve immediately.