Brown the butter in a small saucepan over medium heat, melt the butter until it turns golden brown and gives off a nutty aroma. Browning the butter adds a rich, toasty flavor and extra moisture to the cookies. Let it cool for a few minutes before using.
In a large bowl, whisk together the browned butter, brown sugar, and white sugar until smooth. Add the egg, egg yolk, and vanilla extract. Whisk until the mixture looks creamy and glossy.
In a separate bowl, combine the flour, baking soda, salt, and cinnamon. Gradually add the dry mixture into the wet ingredients, mixing gently until just combined — do not overmix. Fold in the M&Ms and chocolate chips, reserving a few for topping.
In a small bowl, mix the cinnamon and sugar for coating. Roll each cookie dough ball in the cinnamon sugar before placing them on a parchment-lined baking sheet. This adds that classic snickerdoodle flavor and a light crunch on the outside.
Bake at 350°F (175°C) for 8 minutes. Remove the tray and tap it gently on the counter to flatten the cookies slightly — this creates that chewy, crinkled look. Return to the oven and bake for another 5 minutes, or until the edges are golden and the centers still look soft.
Right after baking, gently press in a few extra M&Ms and candy eyes while the cookies are still warm. Let them cool on the tray for a few minutes before transferring to a wire rack to cool completely.