Line the bottom and sides of a deep 8-inch square container with parchment paper. Spread the ice cream into the container, packing firmly. Cover and freeze for 8 hours or until firm.

Preheat the oven to 350 degrees F. Line 2 cookie sheets with parchment paper.

Line a cookie sheet with parchment paper. Prepare the cake mix with egg and almond extract. Pour onto 1 of the prepared cookie sheets. Bake according to the package instructions, or until the center of the cake springs back when lightly touched. Allow to cool.

When the cake has cooled, slice an 8 by 8-inch piece of cake and place in the center of the second prepared cookie sheet. Remove the remaining edges of cake and discard.

Using an electric mixer, beat the egg whites with cream of tartar, salt, and sugar until stiff peaks form.

Turn the molded ice cream out onto the cake. Quickly spread the beaten egg whites over the cake and ice cream, spreading all the way to the parchment paper to seal. Return to the freezer for 2 hours.

Preheat oven to 425 degrees F.

Bake the Alaska on the lowest shelf until the meringue is lightly browned, 8 to 10 minutes. Serve immediately.