Make the biscotti: Preheat oven to 350 degrees Fahrenheit. Line a baking sheet with parchment paper. Set aside.
In a large bowl, combine flour, cocoa, sugar, baking powder, baking soda, cinnamon, and salt. Using a pastry cutter or a fork, cut in butter until mixture is crumbly.
In a separate bowl, whisk eggs, milk, and vanilla until smooth. Pour over dry mixture until dough just comes together.
Turn dough onto a floured surface and very gently knead a few times until dough is smooth and non-sticky. Transfer dough to prepared sheet and pat into a 10-in long log.
Bake biscotti at 350 degrees Fahrenheit for 20 to 22 minutes or until golden brown. Remove from oven and cool 5 minutes. Then, using a serrated knife, cut biscotti into 1-inch thick cookies. Arrange biscotti cut-side down on baking sheet.
Return biscotti to oven and bake 5 minutes. Flip biscotti and bake an additional 5 minutes on the opposite side. Cool biscotti on a wire cooling rack.
Make the glaze: Place cream cheese, powdered sugar, and peanut butter in a medium bowl. Using a handheld electric mixer, beat on medium speed until creamy. Beat in vanilla and just enough milk to achieve a drizzling consistency.