Heat oven to 350°F. Lightly grease cookie sheets. In large bowl, beat butter, granulated sugar and brown sugar with electric mixer on medium speed 1 to 2 minutes or until light and fluffy. Beat in melted chocolate, vanilla and eggs.
On low speed, beat in flour, cocoa and baking soda until mixed. Fold in 1 cup of the vanilla baking chips and the cherries. Drop by rounded teaspoonfuls 2 inches apart on cookie sheets.
Bake 9 to 11 minutes or until set. DO NOT OVERBAKE. Cool 2 minutes. Remove from cookie sheets to cooling racks. Cool completely, about 15 minutes.
Meanwhile, in small microwavable bowl, place remaining vanilla baking chips and oil. Microwave on High 30 seconds; stir. If necessary, microwave in 10 second increments, stirring after each time, until melted and smooth. Spoon drop of mixture in center of each cookie; top each with cherry half. Drizzle remaining mixture over cookies.