Preheat the oven to 350°F. Line baking sheets with parchment paper or leave them ungreased.
In a medium bowl, whisk together 2 1/2 cups all-purpose flour, 1 teaspoon baking powder, 1 teaspoon baking soda, 1 teaspoon cornstarch, and 1 teaspoon salt.
In a large mixing bowl, beat 1 cup softened butter, 1 cup brown sugar, and 1 cup granulated sugar until light and fluffy, about 2–3 minutes.
Add 1 cup peanut butter, 2 large eggs, and 1 teaspoon vanilla extract. Beat until well combined.
Gradually add the dry ingredients to the peanut butter mixture, mixing on low speed just until combined. Do not overmix.
Scoop the dough into 36 equal portions and roll each portion into a ball.
Roll each dough ball in the remaining 1/4 cup granulated sugar and place them on the prepared baking sheets, leaving about 2 inches between each cookie.
Use a fork to gently flatten each dough ball, creating a crisscross pattern on top.
Bake for 10–12 minutes, or until the cookies are lightly golden around the edges.
Allow the cookies to cool on the baking sheet for 5 minutes, then transfer them to a wire rack.
While the cookies cool, melt the 10 ounces chocolate melting wafers according to the package directions. Transfer the melted chocolate to a piping bag or small zip-top bag. Let the chocolate cool for about 5 minutes so it is easier to pipe.
Unwrap 36 chilled Reese's Miniature Peanut Butter Cups. Place one peanut butter cup upside down in the center of each cooled cookie. If needed, use a small amount of melted chocolate to secure each peanut butter cup.
Pipe four chocolate lines on each side of each peanut butter cup to create the spider legs.
Add a small amount of melted chocolate to the front of each peanut butter cup and attach 2 candy eyes.
Allow the chocolate to set completely before serving.