Unwrap the mini peanut butter cups and place them in the freezer while you prepare the cookie dough. This helps them hold their shape when pressed into the warm cookies. Preheat the oven to 350°F and line baking sheets with parchment paper.
Beat the softened butter, brown sugar, and granulated sugar with an electric mixer for 1–2 minutes, until smooth and fluffy. Add the peanut butter, egg, and vanilla and beat again until well combined.
In a separate bowl, whisk together the flour, baking soda, baking powder, and salt. Gradually add the dry ingredients to the peanut butter mixture, mixing just until a soft dough forms. Do not overmix.
Scoop tablespoon-sized portions of dough and roll them into smooth balls. Roll each ball in granulated sugar and arrange them 2–3 inches apart on the prepared baking sheets. Bake for 8–11 minutes, until the edges are lightly golden and beginning to crack.
Immediately press a chilled mini peanut butter cup into the center of each warm cookie. Let the cookies cool on the baking sheet for 15–20 minutes before transferring them to a wire rack so the chocolate center can set.
Melt the chocolate chips with the neutral oil in a microwave-safe bowl, heating in short intervals and stirring between each one until smooth. Transfer the melted chocolate to a piping bag or zip-top bag with a tiny corner snipped off. Pipe four legs on each side of the peanut butter cup.
Dab a tiny amount of melted chocolate onto the backs of the candy eyes and place two eyes on each peanut butter cup. Allow the chocolate to set completely before serving or stacking the cookies.