Preheat the oven to 400 degrees. In a food processor, puree the apricots with the liqueur and cream. Transfer to a bowl.
Beat the egg whites until somewhat stiff, then gradually beat in the sugar and continue to beat until stiff and glossy.
With a rubber spatula, fold half the egg whites into the fruit puree, then fold the puree back into the remaining egg whites; fold until well blended. Spoon the mixture into four 3/4 cup capacity oven proof ramekins or custard cups.
Set cups in a deep baking pan and pour about an inch of hot water, straight from the tap into the baking pan. Set in oven and bake for 30 minutes. Serve immediately.