In a large mixing bowl, beat together the butter and sugar until fluffy. Beat in the egg, egg yolk, and almond extract.
In a separate bowl, combine the flour, salt, and baking soda. Stir with a whisk. Add the flour mixture to the butter mixture. Mix just until moistened. Fold in the slivered almonds.
Spread the batter evenly into a 9-inch pie pan. Bake for 25 to 30 minutes or until lightly browned and cooked through. Cool completely on a wire rack.
Make the frosting: Beat the butter and powdered sugar together until smooth. Add the cherry juice, beat until incorporated. Frost the cookie cake as desired.
Notes
For a stronger cherry flavor, mix ½ cup of drained maraschino cherries into the batter with the slivered almonds. Keep in mind this will change the texture of the cake since the cherries will leak moisture into the batter.