Preheat the oven to 350 degrees F and line a muffin tin with four paper liners.
In a medium bowl, stir together the flour, baking powder, and salt.
In a separate bowl, mix the peanut butter, sugar, egg, and milk until smooth.
Pour the wet mixture into the dry ingredients and stir just until combined.
Divide the batter evenly among the four liners and bake for 18 to 20 minutes, or until a toothpick comes out clean.
Let the cupcakes cool completely in the tin.
Place the chocolate chips and coconut oil in a microwave-safe bowl. Heat in 20-second bursts, stirring each time, until fully melted and smooth.
Spread a thin layer of melted chocolate over each cooled cupcake.
Spoon the remaining chocolate into a small piping bag or zip-top bag with one corner snipped off. Pipe three or four circles on each cupcake, then drag a toothpick from the center outward to create a spiderweb pattern.