Preheat the oven to 350 degrees. Grease a 9-inch square baking pan.
Using a food processor, combine the flour, brown sugar, cornstarch, and salt. Process until blended, about 5 seconds.
Sprinkle the chunks of cold butter over the flour mixture, then add the vanilla. Using pulses, process until the mixture resembles fine crumbs.
Add the pecans and process until finely chopped. Add the toffee bits and process just until incorporated.
Press the dough evenly into the prepared pan. Bake the shortbread just until it begins to color and the edges become golden, about 20 minutes.
About 5 minutes before the shortbread is done baking, melt the chocolate and shortening in the microwave. Stir after 45 seconds, then return to the microwave for 30 more seconds. Stir again to melt the chips. Return to the microwave for another 30 seconds if needed.
After removing the shortbread from the oven, spread the chocolate on top. Let cool completely, then cut into rectangular bars.