Slice two thirds of the strawberries and toss them with ½ cup of the sugar. Puree the remaining berries in a blender with another ½ cup of sugar. Force the puree through a sieve to remove seeds.
Beat the cream with 1 tablespoon of sugar until it holds soft peaks. Stir in the puree, and then fold in the sugared berries. Taste and add more sugar if needed. Serve immediately, or keep refrigerated for up to an hour.