Preheat oven to 350°F. Spray baking sheets with nonstick cooking spray; set aside.
Beat cake mix, milk and almond extract in medium bowl with electric mixer at low speed. Increase speed to medium when mixture looks crumbly; beat 2 minutes or until smooth dough forms. (Dough will be very sticky.)
Coat hands with cooking spray. Shape dough into 1-inch balls. Place balls 2-1/2 inches apart on prepared baking sheets. Flatten each ball slightly. Place cherry in center of each cookie.
Bake 8 to 9 minutes or until cookies lose their shininess and tops begin to crack. Do not overbake. Remove to wire racks; cool completely.
Place white chocolate chips and oil in small microwavable bowl. Microwave on HIGH 30 seconds; stir. Repeat as necessary until chips are melted and mixture is smooth. Drizzle white chocolate mixture over cookies. Let stand until set.