Mix the milk and vanilla extract together in a small bowl; set aside.
Combine the flour and baking powder in a separate bowl.
Beat the peanut butter, brown sugar, and white sugar with an electric mixer in a large bowl until smooth.
Add the eggs one at a time, allowing each egg to blend into the peanut butter mixture before adding the next.
Pour in the flour mixture alternately with the milk, mixing until just incorporated.
Fold in the peanut butter chips; mixing just enough to evenly combine.
Divide the dough into 4 equal parts.
Roll each section into a 4x5-inch rectangle about 1/2-inch thick.
Transfer the dough pieces onto the prepared baking sheets.
Bake in the preheated oven until firm to the touch, about 25 minutes.
Place biscotti loaves on wire racks to cool.
Reduce oven temperature to 300 degrees F (150 degrees C).
Cut each loaf into 1/2-inch slices.
Return the slices to the baking sheets with the cut sides up.
Bake in the oven until biscotti are dry, about 10 minutes on each side.
Cool in the pans for 10 minutes before removing to cool completely on a wire rack.
Melt the chocolate chips in a microwave-safe glass or ceramic bowl in 30-second intervals, stirring after each interval, until melted and smooth, 1 to 3 minutes (depending on your microwave).
Dip the cooled biscotti into the melted chocolate. Set the biscotti onto parchment paper, and allow to set, about 20 minutes.
