In a microwave safe bowl, combine 1 cup white chocolate chips and 2 tbsp vegetable oil. Microwave in 30 second intervals, stirring in-between, until melted and smooth.
Dip each Nutter Butter cookie three quarters of the way into the melted chocolate, scraping any excess chocolate off the back. Place onto a baking sheet lined with parchment paper or a silicone mat.
Add two candy eyes onto each dipped Nutter Butter before the chocolate sets, then transfer to the fridge or freezer for 5-10 minutes or until the chocolate has hardened.
In the meantime, combine remaining chocolate chips with 1 tbsp vegetable oil in another microwave safe bowl. Microwave in 30 second intervals, stirring in-between, until smooth.
Transfer the melted chocolate to a Ziploc bag, snip a tiny piece off one corner, then gently pipe thin lines in multiple directions across each coated cookie, making sure to avoid the eyes.
Return to the fridge or freezer for another 10 minutes to set the chocolate drizzle. Once set, carefully break off the excess candy-coating pieces around each cookie before enjoying!