In a large bowl, sift together the flour, cocoa powder, baking soda, baking powder, and salt. Set aside until needed.
Combine the oil, butter, and chocolate together in a large bowl. Heat in the microwave, in 30 second increments, stirring between increments each time, until the butter and chocolate are completely melted. Set aside and cool while you assemble the other ingredients.
In a large bowl, combine both sugars, eggs, egg yolk, and vanilla and beat until smooth and well combined.
Gradually add in the melted chocolate mixture, adding a little bit at a time and whisking constantly.
Gently fold in the flour in 3 additions, alternating with the sour cream, beginning and ending with the flour. Mix gently and stop when you can still see the lightest trail of dry ingredients.
Pour in the hot coffee (or water) and let it sit for 30 seconds, then fold it into the batter until combined.
Scoop 2 tablespoons of batter into the bottom of each cupcake tin, then press a peanut butter cup into the batter. Top with another 3 tablespoons of batter; each cupcake mold should be 2/3 of the way full.
Bake, one tray at a time, for 16 to 18 minutes, or until the cupcakes have puffed up and a toothpick (or cake tester) inserted in the middle of a cupcake comes out clean, or with a few moist crumbs attached.
Allow cupcakes to cool completely before frosting!
For the Peanut Butter Frosting:
In a large bowl, using a handheld electric mixer, or in the bowl of a stand mixer fitted with the paddle attachment, beat butter on medium-speed until completely smooth. Beat in the vanilla.
Reduce mixer speed to low and slowly add in the sugar, adding a 1/2 cup at a time, beating until the sugar has incorporated into the frosting before adding more. Once all of the sugar has been added, beat in the milk.
Increase mixer speed to medium-high and beat for 3 to 4 minutes, or until the frosting is thick and creamy.
Finally, fold in the beat butter and beat on medium-high for 1 minute. Use a rubber spatula to scrape down the bottom and sides of the bowl, to ensure all ingredients have been combined.