Line a 9x13-inch (approx. 23×33 cm) baking dish with parchment paper. Set aside for later.
In a stand mixer with a paddle attachment, mix the cold butter, powdered sugar, and granulated sugar until well blended. Scrape the sides of the bowl to make sure everything is mixed. Mix in the vanilla extract.
Add the flour in three parts. Make sure each part is fully mixed in before adding the next. Scrape the sides of the bowl as needed.
Press the dough evenly into your lined baking dish. Cover it with plastic wrap and chill in the fridge for at least 30 minutes. You can also leave it overnight.
Preheat your oven to 350°F (180°C), and line baking sheets with parchment paper.
Take the dough out of the fridge and lift it from the baking dish using the parchment paper. Cut the dough into ½ inch squares. Place the squares on the lined baking sheets. Keep them about 1.5 inches apart.
Bake in the oven for 12-14 minutes or until the edges are just starting to turn light brown. Let them cool completely on the tray.
Melt each type of chocolate separately. You can microwave melting wafers on half power for 30 seconds. Then stir. Repeat the process with 15-second increments if needed until the chocolate is smooth.
Drizzle dark chocolate on a third of the bites, milk chocolate on another third, and white chocolate on the last third. Allow the chocolate to set and harden before serving.