Prepare a 9"x9" baking pan by lining with aluminum foil.  Set aside.

Using an electric mixer, beat together peanut butter, and butter until smooth and creamy.  2 cups (475 g) creamy peanut butter, 10 Tablespoons (140 g) salted butter

Add brown sugar and vanilla extract, stir well.2 Tablespoons (25 g) brown sugar, 1 teaspoon (5 ml) vanilla extract

Gradually add powdered sugar, stirring until completely combined.3 ¼ cups (405 g) powdered sugar

Spread peanut butter filling into prepared pan.  To make the surface smooth and even, I like to first spread with the a spoon or spatula, and then lay a piece of wax paper over the filling and use my hands to smooth it out (see video for visual).

Place pan in refrigerator while you prepare your chocolate topping.

To prepare chocolate topping, combine chocolate pieces or chocolate chips and shortening in a small microwave-safe bowl.  Microwave for 20 seconds, stir well, and continue to heat on 15-second increments (stirring well between) until chocolate is completely melted and smooth.4 ounces (115 g) semisweet chocolate, broken into small pieces, 1 teaspoon shortening

Remove bars from refrigerator and spread chocolate evenly over the surface.

Return to refrigerator and chill at least 4 hours, preferably overnight.

Cut and serve.  Keep uneaten bars refrigerated for firmness.