Place the cookies in a food processor. Cover and pulse with several on/off turns until pulverized.
In a medium microwave safe bowl, heat chopped white chocolate in the microwave on medium (50% power) for 1 to 1-1/2 minutes or until melted, stirring once. If not completely melted, repeat heating step, stirring every 30 seconds. Watch closely as scorching can occur. Spoon melted chocolate over doughnut holes. Sprinkle doughnut holes with pulverized cookies before chocolate sets up.