Line the bottom and sides of an 8-inch round mixing bowl or deep 8-inch square container with foil. Spread ice cream in container, packing firmly. Cover and freeze 8 hours or until firm.
Preheat oven to 350 degrees F (175 degrees C). Grease and flour an 8×8 inch pan.
Prepare cake mix with egg and almond extract. Pour into prepared pan.
Bake in preheated oven according to package instructions, until center of cake springs back when lightly touched.
Beat egg whites with cream of tartar, salt and sugar until stiff peaks form.
Line a baking sheet with parchment or heavy brown paper. Place cake in center. Turn molded ice cream out onto cake. Quickly and prettily spread meringue over cake and ice cream, all the way to paper to seal. Return to freezer 2 hours.
Preheat oven to 425 degrees F (220 degrees C).
Bake the Alaska on the lowest shelf, 8 to 10 minutes, or until meringue is lightly browned. Serve at once.