Special equipment: one number 2 round pastry tip
Preheat the oven to 350 degrees F.
In a bowl, whisk together the flour, salt and baking soda.
In the bowl of a stand mixer fitted with the paddle attachment, beat 1/2 cup of the granulated sugar, the peanut butter, brown sugar, butter and oil until light and fluffy. Add the egg and vanilla and beat until combined. Add the flour mixture and mix until the dough starts to come away from the bowl. Scoop portions of the dough onto a parchment-paper-lined baking sheet and refrigerate for at least 1 hour or up to overnight.
Roll the cookies in the remaining 1 cup sugar to coat, then place them onto a parchment-paper-lined baking sheet approximately 1-inch apart. Bake for 8 to 10 minutes, then remove from the oven and carefully place your thumb in the center of each cookie. Return the baking sheet back to the oven and continue baking until the cookies are still soft to the touch and just a touch golden, 2 to 4 minutes. Be careful to avoid over-baking, as the cookies can become dry and tough. Cool the cookies completely.
Melt the milk chocolate chips in the microwave and then place in a small pastry bag fitted with a very small round tip.
Place the peanut butter cups upside-down into the indent of each cookie to create the spider bodies. Pipe a dot of chocolate onto the back of each candy eye and place in the center of the peanut butter cup right next to each other. Pipe 4 chocolate legs on each side of the body. Use the tip of a toothpick to smooth out the legs of the spiders.
Allow the spider legs to set for 5 minutes, and then serve!
You can make these cookies ahead of time and store in an air-tight container for up to 3 days.