Start by making the white chocolate milk. Combine the whole milk and white chocolate chips in a sauce pan over medium low heat. Whisk frequently, until all of the white chocolate chips melt. Then place in a container and chill in the fridge for at least 2 hours.
I think it is easiest to make 2 White Chocolate White Russians at a time. Combine 1 shot kahlua, 2 shots of vodka, and 4 shots of the white chocolate milk in a shaker filled with ice. Place the lid on the shaker and shake for 30 seconds.
Pour the White Chocolate White Russians into 2 glasses filled with ice.