For the cookie dough ball filling, in the bowl of a stand mixer, beat together the butter and both sugars until fluffy. Add in vanilla and milk and mix until combined. Turn the mixer to low and slowly add in the flour and baking soda until fully combined. Stir in the M&M’s.
Roll 1” balls of cookie dough out and place them on a parchment lined cookie sheet. Freeze at least 30 minutes, until hardened.
To make the peanut butter cookie dough, in a medium bowl, stir together the peanut butter, salted butter, sugar, brown sugar egg and vanilla and mix until combined. In a separate bowl, sift together the flour and baking soda. Slowly stir the dry ingredients into the wet ingredients until fully combined. Place in fridge at least 30 minutes to harden slightly.
To form the cookies, remove the frozen cookie dough balls from the freezer and the peanut butter cookie dough from the fridge; take a small handful of the peanut butter dough and place on one side of the frozen cookie dough ball, and do the same to the other side to make a sandwich around the cookie dough ball and pinch the edges together to seal the cookie dough ball within the peanut butter dough.
Repeat with the remaining peanut butter dough until you are out of peanut butter dough. You will have remaining frozen M&M cookie dough balls, so do as you wish with those.
Bake in a 375°F oven until edges of cookies are lightly golden brown, roughly 10-12 minutes.
Remove and allow to cool before eating.