In a food processor with the knife blade attached, pulse 1 cup frozen strawberries until finely chopped. Transfer the chopped berries to a large metal bowl.
Add the yogurt, sugar, vanilla and remaining strawberries to the food processor and puree until smooth. Transfer to the bowl with the frozen strawberries and stir until well combined. Cover and freeze until firm but not hard, about 1 hour. Garnish with fresh strawberries.
The Greek yogurt provides an especially creamy texture, but if you like, you can swap in low-fat yogurt to further reduce your calories and fat.