Slice the strawberries. In a large bowl, toss 3/4 of them with the sugar and orange liqueur. Refrigerate for at least 1 hour to macerate.
Put the ice cream in the refrigerator to soften.
Put the cream and half of the macerated strawberries in a cold mixing bowl. With an electric mixer, whip to soft peak, about 2 minutes. Fold in the softened ice cream.
Distribute the cream among 6 chilled bowls. Mix the plain sliced berries with the remaining macerated berries and place on top of the cream.