Preheat oven to 400°F (204°C). Line two baking sheets with parchment paper and set aside.
Using a stand mixer fitted with the paddle attachment, combine cold butter, brown sugar, and granulated sugar. Beat on medium speed until creamy and no visible butter chunks remain.
Add the eggs one at a time, mixing until combined. Add the vanilla extract and continue mixing, scraping down the sides of the bowl as needed.
In a medium bowl, whisk together the all-purpose flour, cake flour, salt, baking powder, and baking soda.
With the mixer on low speed, gradually add the flour mixture to the wet ingredients. Mix until almost fully combined.
Add the M&Ms and mini M&Ms. Mix just until incorporated and the M&Ms are evenly distributed.
Divide the dough into 8 large balls.
Place 4 cookie dough balls onto each lined baking sheet, spacing them out evenly.
Bake for 12-13 minutes, or until the edges are golden brown.
Let the cookies cool on the baking sheet for 10 minutes before transferring to a wire rack.
Serve warm.