MIX butter, sugar and almond extract thoroughly using an electric mixer. Gradually blend in flour and corn starch. Add cherries and chocolate.
FORM into 1-inch balls and place on ungreased baking sheets. Pour sugar on a small plate; dip bottom of drinking glass in sugar and gently press down on each cookie to flatten.
BAKE in a preheated 300°F oven for 20 to 30 minutes, or until bottoms begin to brown.
COOL 5 minutes; remove to a wire rack to cool completely.
PLACE 2 ounces chocolate and shortening in a small resealable plastic bag. Microwave on HIGH for about 30 seconds, until chocolate is melted. Snip off corner and drizzle over cookies.