In a large mixing bowl, combine the softened butter and creamy peanut butter. Use an electric mixer to blend these together until smooth and creamy.
Gradually add in the powdered sugar and vanilla extract to your peanut butter mixture. Mix until fully combined.
Line an 8x8 inch baking dish with parchment paper. Spread your peanut butter mixture evenly into the bottom of the dish, pressing firmly.
In a microwave-safe bowl, combine semi-sweet chocolate chips and vegetable oil. Microwave in short bursts, stirring in between until melted and smooth.
Once melted, carefully pour the chocolate mixture over your pressed peanut butter layer in the baking dish. Use a spatula to spread it evenly across the top.
Cover the dish with plastic wrap and refrigerate for at least two hours until set.
Once set, remove from the refrigerator and lift out using the parchment paper edges. Cut into squares or bars, serve them on a platter.