Line an 8x8 inch pan with parchment paper or aluminum foil and set aside.
In a large mixing bowl, mix together butter and brown sugar until it is fluffy. This takes about 3 minutes. Add vanilla and bet until combined.
Turn the mixer to low and alternate the flour and the sweetened condensed milk until combined. Gently fold in chocolate chips.
Press the cookie dough into the bottom of the 8x8 pan. It will be sticky so lightly flour your hands if needed.
Cover your bars with plastic wrap and refrigerate for 3 hours or overnight until firm.
To make the topping, combine the peanut butter and 1/2 cup chocolate chips in a microwave safe bowl. Stir every 30 seconds until smooth. Pour and spread over the top of the chilled dough and chill at least for 1 hour until firm.