Line 1 (9-inch) cake pan with plastic wrap, with 3 inches overhanging. Spread softened ice cream into lined pan in a smooth, even layer. Freeze for 3 hours, or until frozen solid.
Preheat oven to 350 degrees F.
Butter and flour 2 (10-inch) round cake pans and set aside. In a stand mixer or with a hand mixer, beat cake mix, water, oil and eggs in a large mixing bowl on medium speed for 2 minutes, or until well blended. Using a spatula, divide batter between the 2 prepared cake pans. Bake for 25 minutes, or until a toothpick inserted into the center comes out clean. Let cakes cool in pans on a wire rack for 15 minutes. Run a knife around the edge of each pan to loosen cakes and remove from pans.
While cakes are cooling, heat heavy cream in a small heavy saucepan over medium heat until bubbling around the edges. Remove pan from heat, add chocolate morsels, and stir with a whisk until smooth. Refrigerate for about 30 minutes, until cool and slightly thickened, stirring occasionally. Spread ganache on top of and around sides of both cake layers, keeping layers separate and not fitting together yet. Refrigerate entire cake for 1 hour, or until ganache is set.
Place 1 cake layer, ganache side up, on a serving platter. Remove ice cream from pan, peel off plastic wrap, and place on top of cake layer. Place second cake layer on top of ice cream, ganache side up. Freeze until ready to serve, but let stand at room temperature 5 minutes before seving.