Position a rack in the center of the oven and preheat to 350 degrees F. Line a 12-cup muffin pan with paper liners.
Heat the coffee and milk in a small saucepan over medium heat until it just comes to a simmer, 2 to 3 minutes. Turn off the heat, and then whisk in the cocoa powder until smooth. Transfer to a large bowl. Let cool slightly, about 5 minutes.
Whisk together the flour, baking soda and salt in a medium bowl.
Whisk the sugar, oil and vanilla into the coffee milk mixture until completely blended. Then whisk in the egg until smooth. Whisk in the flour mixture until just combined.
Divide the batter among the muffin cups with 1/4 cup ice cream scoop (about 3 tablespoons each). Bake until the tops spring back when lightly pressed and a toothpick inserted into the center of a cupcake comes out mostly clean (a few moist crumbs are fine), 20 to 25 minutes.
Let cool for 10 minutes in the pan set over a cooling rack, and then remove the cupcakes directly to the cooling rack to cool completely.
Meanwhile, place the peanut butter chips in a heat-safe medium bowl. Heat 3/4 cup of the heavy cream in a small saucepan over medium heat until it just starts to simmer, about 2 minutes. Pour the hot heavy cream over the peanut butter chips, shaking the bowl to ensure the chips are submerged, and let sit for a minute. Stir the mixture together until smooth and well blended, and then stir in the remaining 1/4 cup cold heavy cream.
Place in the refrigerator until it thickens to the texture of stiff peanut butter, about 20 minutes.
Beat the mixture with an electric hand blender until it just gets fluffy and lightens in color, about 2 minutes; do not overbeat or there is a chance the heavy cream will start to break.
Spread a scant 1/4 cup of frosting on each cooled cupcake (Tip: Use an ice cream scoop to ensure all the cupcakes get the same amount of frosting). Then top each with a chocolate-covered peanut butter cookie. Serve immediately.