Sift flour, baking soda and salt in a bowl. Set aside. In a large bowl, or bowl of you stand mixer, cream together butter, peanut butter, granulated sugar and brown sugar.
Whisk in milk, vanilla extract and egg. Gradually add flour, in 2-3 additions, and beat until the dough comes together. It should be smooth and soft. Cover the bowl and refrigerate the dough for about 1 hour, so it's easier to roll.
Preheat oven to 375°F (190°C) and line two cookie sheets with parchment paper. Set aside.
Divide the dough into 30 equal pieces, then roll them into balls. Roll each in Demerara sugar and place on your cookie sheet about 2 inches (5 cm) apart. Bake for 10 minutes, until golden brown around the edges, but still puffy in the center.
Remove cookies from oven (and put the other sheet into the oven) and immediately top each with a chocolate piece. Press it into the center of the cookie very lightly, just so the cookie cracks a bit.
Allow the cookies to cool at room temperature until the chocolate is completely hard again, then store them in airtight containers for up to a week.