Pre-heat oven to 350°F or 325°F for glass bake ware.
In a medium bowl, cream butter, sugar and vanilla until light and fluffy.
Add the eggs, vanilla and almond extracts; beat well.
In a small bowl, sift together the flour and baking powder.
Add dry ingredients to the creamed mixture, folding to combine well.
Fold in the chopped cherries.
Spread in a parchment lined or greased 9-inch square baking pan.
Place in the the pre-heated oven and bake for 45 - 55 minutes or until a toothpick inserted in the center comes out clean.
Remove from oven and cool completely on a wire rack.
Frost with vanilla frosting.
To prepare the vanilla frosting:
In a medium bowl, beat together the butter, confectioners' sugar, vanilla and milk until, light, fluffy and of a good spreadable consistency.
Add the milk only a little at a time until the proper consistency is achieved.
To assemble the squares:
Spread over the cooled cookies and cut into squares or bars.
These freeze very well in airtight containers.
Notes
This recipe is too large for an 8-inch x 8-inch pan; if you do not have a 9-inch x 9-inch pan, you can multiply the entire recipe by 1-1/2 and use a 9-inch x 13-inch pan instead.