Preheat the oven to 350°F (175°C).

In a bowl, whisk together the flour, baking soda, and salt.

In a separate bowl, cream together the softened butter, brown sugar, and granulated sugar until smooth.

Beat in the eggs one at a time, then stir in the vanilla extract.

Gradually blend the dry ingredients into the wet mixture.

Fold in the milk chocolate chips and white chocolate chips.

Drop dough by rounded tablespoons onto ungreased cookie sheets.

Bake for 10 minutes or until lightly golden. Let cool on the baking sheets for a few minutes before transferring to wire racks.