This is Cookie Society co-owner Marissa Allen's go-to shortbread recipe, but with toffee pieces thrown in. She likes to roll the dough into logs and store it in the freezer. Let it warm up on the counter for about an hour, then slice and bake!
In a large bowl, using an electric mixer, mix the butter, sugars, and vanilla on medium-high until smooth, about 4 minutes. Add the flour, salt, and toffee pieces. Mix until combined, about 1 minute.
Dump the dough onto a floured work surface. Roll into a 1 1/2-inch-diameter log or shape into a flat disk. Wrap tightly in plastic wrap; chill until firm, at least 30 minutes.
Preheat the oven to 350°.
If using a log of dough, cut into 1/2-inch-thick slices. If using a dough disk, roll out on a lightly floured work surface to 1/2 inch thick. Using a cookie cutter, cut out the cookies. Divide the cookies between 2 rimmed baking sheets lined with parchment, spacing the cookies 2 inches apart. Bake until the edges just begin to brown, 15 to 20 minutes. Let the cookies cool completely on the baking sheet.
Once cool, dip the cookies in the melted chocolate or drizzle it on top. Let sit until the chocolate sets, about 30 minutes.