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.