Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.
In a large bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy.
Beat in the egg and vanilla extract until well combined.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
Gradually mix the dry ingredients into the wet ingredients until just combined. Do not overmix.
Fold in the red, white, and blue M&Ms and white chocolate chips using a spatula.
Scoop 1.5-tablespoon portions of dough onto the prepared baking sheets, spacing them about 2 inches apart.
Bake for 10 to 12 minutes, or until the edges are lightly golden but the centers are still soft.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.