Position racks in the upper and lower thirds of the oven and preheat to 350 degrees F. Spread the pecans on a rimmed baking sheet and bake until slightly darkened, about 10 minutes; let cool completely. Transfer to a food processor and pulse until finely ground - do not over-pulse, as you don't want a paste.

In a medium bowl, combine ½ cup confectioner's sugar, flour, salt, vanilla, and ground pecans; cut the butter into the flour mixture using a pastry cutter or two forks until well combined.

Transfer the cookie dough to a medium bowl, cover it tightly, and chill in the refrigerator for at least 30 minutes. If chilling for 3+ hours, make sure you let the cookie dough sit at room temperature for at least 30 minutes before rolling it into balls; the cookie dough will be very stiff after being in the fridge that long.

Preheat the oven to 350°F and Line two baking sheets with parchment paper; set aside. Scoop into rounded tablespoon-sized rounds and roll between your hands into balls, and arrange them on the prepared baking sheets at least 1 to 2 inches apart.

Bake, switching the position of the pans halfway through, until lightly golden on the bottom, 15 to 20 minutes. (While waiting for the other Pecan snowball cookies to bake, place the prepared baking sheets with the cookies in the freezer).

Let the Pecan Snowballs cookies cool for about 5 minutes on the baking sheet, then gently roll them in the confectioners' sugar to coat thoroughly. Be careful when handling pecan snowball cookies, as they are very fragile. Next, place the Pecan Snowballs Cookies on wire racks to cool completely; it's best on a wire rack so the powdered sugar doesn't become moist. When fully cool, roll again with the confectioner's sugar.