In a large bowl of a stand mixer, combine the cold, diced butter with the confectioners' sugar. Beat the mixture until it is smooth and creamy, ensuring to frequently scrape down the sides of the bowl to incorporate all ingredients evenly.
Add the vanilla extract and salt to the butter mixture. Gradually introduce the flour at a low speed, mixing until the dough just begins to form. Be cautious not to overmix.
Fold in the toffee bits and chopped pecans into the dough. Divide the dough into two equal portions. Form each portion into a log approximately 6 ½ inches in length and 1 ½ to 1 ¾ inches in diameter. To avoid air pockets and achieve a uniform density, compress the dough firmly. On a lightly floured surface, roll each log to the specified dimensions.
Wrap each log of dough tightly in plastic wrap and refrigerate for 1 hour, or until the dough is sufficiently chilled.
Preheat the oven to 350 degrees Fahrenheit. Remove the shortbread dough from the refrigerator. On a parchment-lined baking sheet, slice each log into 14-15 pieces, each being less than ½-inch in width. Arrange the slices on the baking sheet and bake for 12-16 minutes, or until the edges start to turn a light golden brown.
Once baked, remove the cookies from the oven and allow them to cool completely on a wire rack.