Blend 2 cups of the strawberries, and 1/2 cup of the sugar in a blender or food processor until smooth. Transfer to medium saucepan and cook over medium heat until bubbling and just thickened. Set aside to cool, then refrigerate and chill for about 1 hour. Stir in remaining 1 cup strawberries.
In a medium clean, cold bowl, beat cream with the remaining 2 tablespoons of the sugar and liqueur until stiff peaks form. Fold the whipped cream into strawberry mixture. Chill fool until beginning to set, about 30 minutes.