Purée 3 cups of fresh raspberries (reserve the rest for garnish) and simple syrup in a food processor or blender. Add additional syrup and lemon juice to taste.
Strain mixture for seeds (or leave them in for a more rustic flavor) and pour into a shallow dish. Freeze until mostly firm, approximately 2 hours.
Remove and stir with large fork to break up crystals and re-mix ingredients. Return to freezer until ready to serve