Prepare the nougat filling: In a bowl, cream together softened butter and powdered sugar until smooth. Stir in peanut butter and vanilla extract. Press this mixture evenly into the bottom of a parchment-lined 8x8 inch baking pan.
Make the caramel layer: In a saucepan, combine sweetened condensed milk, corn syrup, brown sugar, and butter. Cook over medium heat, stirring constantly, until the mixture reaches the soft-ball stage (235°F / 113°C). Remove from heat and stir in vanilla extract. Pour the caramel evenly over the nougat layer.
Chill the bars: Place the pan in the refrigerator for at least 1 hour, or until the caramel is firm.
Cut and coat the bars: Once firm, lift the block from the pan using the parchment paper and cut into desired bar shapes. Melt the chocolate chips and vegetable oil together in a microwave-safe bowl, stirring every 30 seconds, until smooth. Dip each bar into the melted chocolate, ensuring it's fully coated. Place coated bars on a parchment-lined baking sheet.
Set the chocolate: Allow the chocolate to set at room temperature or in the refrigerator until firm.
Notes
Store homemade candy bars in an airtight container at room temperature or in the refrigerator.