Line an 8 x 8 baking dish, with straight sides, with parchment paper. Spray the parchment paper with cooking spray. Set aside.
In a large mixing bowl add the butter and brown sugar. Beat with a hand mixer until light and fluffy. Add vanilla extract and continue to beat for an additional minute.
Add flour and sweetened condensed milk, alternating between the two while mixing, on the low speed setting. Beat together until combined and a soft dough forms.
Using a spatula fold in the chocolate chips and M&M's into the dough.
Spread the dough out in an even layer in the 8 x 8 prepared baking dish.
Put the bars in the freeze for 30 minutes while making the chocolate topping.
In a small mixing bowl add the butter and chocolate chips. Place the bowl in the microwave for 30 seconds. Remove and stir. Place back in the microwave and repeat steps until chocolate is melted and smooth.
Remove the bars from the freezer and pour the melted chocolate evenly over the top of the cookie dough. Sprinkle additional M&M’s over the top of the chocolate and gently press them down into the melted chocolate.
Place the cookie dough bars in the refrigerator and chill for 2 to 3 hours, or until ready to serve.