Roughly chop the dried cherries and transfer them to a small bowl. Add the amaretto and let sit for one hour until plumped. Strain the cherries, reserving the amaretto for another use (a cocktail, perhaps)
Beat the egg whites until soft peaks form.
In a small heavy saucepan, combine the honey, sugar and water. Heat over low heat, stirring constantly until the sugar is dissolved. Bring the mixture to a boil and cook for an additional 2 minutes. In a slow, steady, thin stream beat the honey mixture into the egg whites. Continue beating until the meringue cools, about five minutes. Meringue should be glossy and relatively stiff.
In a separate bowl, beat the cream and almond extract until it's the consistency of sour cream. Fold in the almonds, pistachios and dried cherries to the cream. Add the cream mixture to the meringue and with a rubber spatula, gently fold it in until completely combined.
Transfer the mixture to a freezer safe container. Cover and freeze until firm.