Line a 9x13 baking dish with parchment paper. Set it aside.
Using either a stand mixer, or a medium size mixing bowl and a handheld mixer on medium-high speed, beat the softened butter for 1 minute, until smooth.
Add the peanut butter and vanilla. Continue mixing for 1 minute, until smooth.
Lower the mixer speed to medium-low and add the powdered sugar 1 cup at a time, mixing well after each cup. Increase the mixer speed to medium-high and continue mixing until completely incorporated.
Using either a silicone spatula, or an offset spatula, evenly spread the peanut butter mixture in the bottom of the prepared baking dish.
Add the chocolate chips and oil to a small microwave safe bowl. Heat for 1 minute, stir, and continue to mix in 15 second intervals until the mixture is completely smooth.
Using a silicone spatula, or an offset spatula, evenly spread the chocolate over the peanut butter layer. Cover and chill the refrigerator for 15 - 20 minutes.
Remove the baking dish from the refrigerator. Carefully slice the buckeye bars into 15 - 2 ½ in x 3 in slices. Cover the baking dish and return the bars to the refrigerator to continue chilling for an additional 1 hour 45 minutes.
Remove the bars from the dish by the parchment paper. You may need to carefully re-slice the bars. Serve immediately.
To Store: Store any leftovers in an airtight container at room temperature for up to 2 weeks.
To Freeze: You can freeze the bars for up to 3 months. Allow the bars to thaw in the refrigerator overnight before serving.
For easier clean-up line your baking dish with parchment paper before baking. This will allow you to easily lift them out of the pan and slice for serving.
Use processed peanut butter in this recipe, not natural peanut butter. The oils separate in natural peanut butter and it doesn’t hold as nicely together as the processed version does.