Place butter, confectioners' sugar, and vanilla in a large bowl. Beat together on medium speed until the mixture is very smooth, about 1 minute. Do not beat until light and fluffy. Add the flour, and mix on low speed only until the flour disappears into the dough, about 1 minute. Don't work the dough much once the flour is incorporated. Fold in the toasted pecans with a wooden spoon or sturdy rubber spatula. (See Note 2)
Using the spoon or spatula, transfer the dough to a gallon-size ziploc bag. Put the bag on a flat surface. Leaving the top open, roll the dough into a 1/4-inch thick rectangle that completely fills the bag. As you roll, turn the bag occasionally and lift the plastic from the dough so that it doesn't cause creases. Seal the bag, and place in refrigerator or freezer for at least 2 hours, or for up to 2 days. (See Note 3)
Preheat the oven to 325° F. Line two baking sheets with parchment paper or silicone mats.
Put the ziploc bag on a cutting board and slit it open. Turn the firm dough onto a parchment lined board or counter; discard the bag. Using a ruler as a guide and a pizza cutter or sharp knife, cut the dough into 1-1/2 inch squares. Transfer the squares to the baking sheets and carefully prick each one twice with a fork, gently pushing the tines through the cookies until they hit the baking sheet. Refrigerate for 20 minutes. (See Note 4)
Bake at 325° F for 20 to 25 minutes, rotating the sheets from the top to bottom and front to back at the midway point. The cookies will be very pale - they shouldn't take on much color. Transfer the cookies to a rack to cool.
If desired, dust the cookies with confectioners' sugar while they are still hot. Cool the cookies to room temperature before serving. Yield: 4 dozen cookies. (See Note 5)