Preheat oven to 375 degrees Fahrenheit (190 degrees Celsius) and line baking sheets with parchment paper.

In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar until the mixture is light and fluffy.

Beat in the eggs one at a time, followed by the vanilla extract, ensuring each is fully incorporated.

In a medium bowl, whisk together the all-purpose flour, baking soda, and salt.

Gradually add the dry ingredients to the wet mixture, stirring until just combined.

Fold in the white chocolate chips and semi-sweet chocolate chips using a spatula.

Drop rounded tablespoons of dough onto the prepared baking sheets, spaced approximately 2 inches apart.

Bake for 9 to 11 minutes or until the edges are lightly golden but the centers remain soft.

Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.

Once the cookies are entirely cool, use a fine-mesh sieve to dust the tops generously with confectioners' sugar.