Heat oven to 375F (190C). Line cookie sheet with parchment paper.
Chop the Mars Bars into small pieces and set aside.
In the bowl of a stand mixer (or using a handheld mixer), cream room temperature butter and brown and granulated sugars together on medium speed until smooth, about 2 minutes.
Add the egg and egg yolk, vanilla, baking soda and salt and continue to cream for 1 minute.
Remove the bowl from the stand mixer and gently fold in the flour until just combined.
Fold in the chocolate chips.
Chill the dough in the fridge, covered with plastic wrap for 15 minutes to make it easier to stuff.
Remove the bowl from the fridge and scoop out 1 tablespoon of dough. Flatten it in the palm of your hand. Drop a few pieces of Mars Bar onto the dough then scoop out another tablespoon of dough and cover the Mars Bar pieces. Press into a ball taking care to cover all of the chocolate bar pieces.
Bake on the parchment lined cooking sheet on the centre rack of the oven. Start checking the cookies at 12 minutes. They can take anywhere from 12 - 17 minutes to bake depending on your oven. Look for smooth golden tops.