Preheat oven to 350°. Divide blackberries and peaches between 8 lightly greased 6-oz. custard cups (about 1/3 cup per custard cup).
Pour melted ice cream into flour in a slow, steady stream, whisking constantly until smooth; whisk in eggs. Pour mixture over fruit in custard cups. Top with sugar cookies. Place custard cups on a 15- x 10-inch jelly-roll pan.
Bake at 350° for 20 to 25 minutes or until custard is set. Cool on pan 40 minutes.
Note: For testing purposes only, we used Häagen-Dazs Vanilla Ice Cream and Pepperidge Farm Sugar Home Style Cookies. We also tested with Blue Bell Homemade Vanilla Ice Cream.