In food processor, crush Tim Tams until they resemble fine crumbs.
Add the cream cheese and Kahlua and process a few times until all combined.
Place in a container and refrigerate 20 minutes to get firm.
Roll into 1 inch balls and place on a parchment paper lined container in the refrigerator for another 20 minutes.
Place the cup of white chocolate and 1/4 cup milk chocolate in microwave safe bowl.
Microwave 30 seconds at a time, stirring at each interval, until chocolate is melted and smooth. This may take 2-3 minutes.
Dip each truffle in the melted chocolate and place back on parchment paper.
Place back in refrigerator to harden about 1 hour.
Melt the remaining white chocolate and drizzle over each truffle.