1. Preheat oven to 350 degrees F.In a large mixing bowl, cream together butter and sugar.
2. Mix in flour, baking powder and salt at a low speed, followed by the vanilla and milk. The dough should come together into a soft ball.Take a tablespoon full of dough and flatten it into a disc about 1/4-inch thick.
3. Place on a parchment-lined baking sheet and repeat with remaining dough. Cookies will not spread too much, so you can arrange them fairly closely together.
4. Bake cookies for 11-13 minutes, until bottoms and the edges are lightly browned and cookies are set.Immediately after removing cookies from the oven, use your thumb or a small spoon to make a depression in the center of each cookie. Cool for a few minutes on the baking sheet then transfer to a wire rack to cool completely.To make filling, whisk together peanut butter, confectioners’ sugar, salt and vanilla in a small microwave-safe bowl. When the mixture has come together, heat it in the microwave (in short intervals, stirring frequently), until it is soft. Working carefully with the warm filling, transfer it to a pastry bag (or plastic bag with the tip cut off) and pipe a generous dome of the filling into each cookie’s “thumbprint”.Chill filled cookies for 20-30 minutes, or until the peanut butter is firm.Melt the chocolate and cocoa butter in a small, heat-resistant bowl placed over a small saucepan filled with simmering (not boiling) water.Dip chilled cookies into chocolate, let excess drip off, and place on a sheet of parchment paper to set.