Preheat oven to 350°. Line a 9- by 13-inch baking pan with foil so that the ends extend over the edges of the pan by at least 2 inches.
In the large bowl of an electric mixer, beat the butter, peanut butter, sugar, and egg yolk on medium-high speed until the mixture is smooth and creamy, about 2 minutes, scraping down the sides of the bowl if necessary. Add the flour, oats, and salt and beat the mixture on low until the ingredients are just blended, about 30 seconds.
Press the mixture evenly into the bottom of the prepared pan. Bake the crust until it is golden brown, 15 to 20 minutes (be careful not to overbake).
Remove the pan from the oven and scatter the chocolate chips evenly over the crust. Return the pan to the oven for 1 minute. Remove the pan again and, using a small spatula, spread the chocolate evenly over the crust.
Sprinkle the toffee pieces over the chocolate, gently pressing them into place.
Set the pan on a wire rack to cool until the chocolate has set, about 2 hours. Using the edges of the foil, lift the dessert from the pan, then cut it into rectangles.
Tips:For maximum freshness, store the bars in the refrigerator.