Preheat oven to 250°F. Line a large baking sheet with parchment paper. Using a cake pan as a guide, draw two 8-inch circles; invert paper. Mix dried cherries and rum; set aside. Mix espresso and boiling water; set aside.
Using an electric mixer, beat egg whites, cream of tartar and salt until soft peaks form. Beat in sugar, and then beat at high speed until stiff. Beat in espresso and vanilla.
Spread egg-white mixture into 2 even disks in prepared parchment circles. Bake for 1 1/2 hours, then turn off oven and let stand in oven for 1 hour. Let cool. Peel off paper and place 1 meringue layer in a 9-inch springform pan.
Drain cherries; pat dry. Stir into vanilla ice cream; spread into pan. Top with second meringue; freeze for 30 minutes. Combine chocolate ice cream and nuts; spread onto meringue. Cover with plastic wrap; freeze for 1 hour.
Remove cake from pan. Whip heavy cream and spread on top. Dust with cocoa and garnish with cherries.