Preheat oven to 375 degrees F (190 degrees C). Line a baking sheet with a silicon mat or parchment paper.
Mash the butter, white sugar, and brown sugar together in a large mixing bowl with a spatula until creamy and smooth, 2 to 3 minutes. Add the egg and vanilla; whisk vigorously for 20 to 30 seconds.
Whisk the flour, salt, and baking soda together in a small bowl; dump into the butter mixture and mix until just combined. Fold the semi-sweet chocolate chips, white chocolate chips, and milk chocolate chips into the mixture. Arrange onto the prepared baking sheet using a small scoop or large spoon.
Bake in the preheated oven until golden brown, about 10 minutes; remove from oven and allow to cool on the sheet for 10 minutes. Transfer to a wire rack to finish cooling completely.