Put the hulled strawberries in a bowl and set aside. Cut off and discard the tops of the 12 large strawberries and trim the bottoms so that they sit upright. Use a small melon baller to scoop out the inside of each strawberry to make a small cup, adding the scooped flesh to the bowl with the hulled strawberries. Wrap and store the berry cups in the refrigerator until ready to assemble.
Combine the rose, sugar and bowl of strawberries and scooped flesh in a blender and blend on high until smooth. Strain through a fine-mesh sieve into an 8-inch square metal pan. Freeze 3 to 4 hours, scraping the mixture with a fork every hour to make it slushy. Wrap and freeze until ready to serve. The granita can be made a day ahead and stored overnight.
Working in batches, remove the strawberry cups from the refrigerator and fill with a spoonful of the granita, mound some more on top and top with a sprig of mint. Store the assembled granita cups in the freezer while assembling the remaining cups to prevent them from melting.
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