Preheat the oven to 350°F (175°C) and line a standard muffin tin with cupcake liners.
In a large mixing bowl, combine the flour, sugar, cocoa powder, baking soda, baking powder, and salt. Whisk until well combined.
In another bowl, whisk together the egg, buttermilk, vegetable oil, and vanilla extract.
Gradually add the wet ingredients to the dry ingredients, mixing until just combined. Carefully stir in the boiling water until the batter is smooth.
Pour the batter evenly into the prepared cupcake liners, filling each about two-thirds full.
Bake for 18-20 minutes, or until a toothpick inserted into the center comes out clean. Allow the cupcakes to cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.
While the cupcakes are cooling, prepare the peanut butter frosting by beating the softened butter and peanut butter together until creamy.
Gradually add the powdered sugar, alternating with the heavy cream, and beat until smooth and fluffy. Stir in the vanilla extract.
Once the cupcakes are completely cool, frost them generously with the peanut butter frosting using a spatula or piping bag.