Preheat the oven to 325°F (165°C) and line a 9x9 inch baking pan with parchment paper, leaving an overhang on the sides.
In a medium bowl, whisk together the flour, baking soda, and salt until well combined.
In a large bowl, stir together the melted butter, brown sugar, and granulated sugar until no lumps remain.
Add the egg, egg yolk, and vanilla extract to the butter mixture and whisk vigorously until the batter looks shiny.
Fold the dry ingredients into the wet ingredients using a spatula until just a few streaks of flour remain.
Stir in the chocolate chips and 3/4 cup of the M&M candies.
Press the dough evenly into the prepared baking pan using a spatula or floured hands.
Sprinkle the remaining 1/4 cup of M&M candies over the top and press them lightly into the surface.
Bake for 25 to 30 minutes, or until the edges are golden brown and the center is set but still soft.
Remove from the oven and allow to cool completely in the pan for at least 1 hour before lifting out by the parchment and slicing into 16 bars.