Preheat the oven to 350 degrees Fahrenheit. Line an 8"x8" pan with parchment paper so it hangs over the edges. Press it down inside.
In the bowl of an electric mixer, mix together cake mix, egg, melted butter, and vanilla extract. Quickly mix in 3/4 c. Reese's Peanut Butter Chips.
Press mixture evenly into prepared pan. Bake for approximately 12-14 minutes, or just until set. Don't over bake or they'll be dry!
Let them cool on a cooling rack. Melt 1/2 c. Reese's Peanut Butter Chips in the microwave (in short increments, stirring between, so it doesn't burn) and drizzle over the top of the cooled bars. Let the melted peanut butter chips set up, then slice and enjoy!