Make the Cookies:

Preheat your oven to 350°F (177°C) and line two baking sheets with parchment paper.
Melt the chocolate chips, vegetable oil, and instant coffee in a microwave-safe bowl in 30-second intervals, stirring each time until smooth.
In a stand mixer with a whisk attachment, whisk eggs and sugar on medium-high until thick and light in color (about 5 minutes).
In another bowl, sift together cocoa powder, flour, baking powder, and salt.
Add vanilla to the egg mixture, then fold in the melted chocolate. Gently mix in the dry ingredients until just combined. Let the batter rest at room temperature for 30 minutes.
Scoop the batter by tablespoonfuls onto the prepared baking sheets. Bake for 5-7 minutes, or until the cookie centers are set. Let cool on the sheet for 2 minutes, then transfer to a cooling rack.
Make the Frosting + Assemble:

In a bowl, cream together the butter and peanut butter. Mix in vanilla and powdered sugar. Gradually add milk until the frosting is pipable.
Pipe frosting onto half of the cookies and top with another cookie to form sandwiches.