Preheat your oven to 350°F (175°C). This ensures that your cookies bake evenly.
In a large mixing bowl, cream together the softened unsalted butter, light brown sugar, and granulated sugar until light and fluffy, about 2-3 minutes.
Beat in the large egg and vanilla extract until well combined.
In a separate bowl, whisk together the all-purpose flour, instant vanilla pudding mix, baking soda, and salt.
Gradually add the dry ingredients to the wet mixture, mixing until just combined. Be careful not to overmix.
Gently fold in the semi-sweet chocolate chips and 3/4 cup of the milk chocolate M&Ms. The dough will be thick.
Using a cookie scoop or tablespoon, drop mounds of dough onto the prepared baking sheet, spacing them about 2 inches apart.
Press a few of the remaining milk chocolate M&Ms on top of each cookie mound.
Bake in the preheated oven for about 10-12 minutes, or until edges are lightly golden but centers are still soft. They will continue to cook on the baking sheet.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.