Preheat your oven to 350°F and line a large baking sheet with parchment paper.
Spread your chopped pecans in a dry skillet over medium heat. Toast for 3 to 4 minutes, shaking the pan constantly, until fragrant and golden. Pro Tip: Toasting the pecans drives off internal moisture and coaxes out the natural oils. For an ultra-tender "melt-away" texture, cool the toasted nuts completely, then pulse half of them in a small food processor until they resemble a coarse meal before mixing them into the flour.
In a large bowl, combine the softened butter, ½ cup of powdered sugar, vanilla extract, and salt. Use an electric hand mixer or stand mixer to blend until completely smooth and creamy (about 1 to 2 minutes).
Add the all-purpose flour to the butter mixture. Blend on low speed just until a cohesive dough forms. Fold in the finely chopped and ground pecans with a wooden spoon or spatula until evenly distributed.
The Shaping Secret: Dampen your palms slightly with cold water to keep the eggless dough from binding to your skin. Pinch off portions and roll them tightly between your hands to shape exactly 36 uniform, tight round balls.
Arrange the dough balls on your parchment-lined sheet pan, leaving about an inch of space between each. Bake for 12 minutes. The Bottom-Doneness Test: Do not look for browning on top; snowball cookies should remain quite pale. Carefully lift one cookie with a spatula at the 12-minute mark—the bottom should be a light, delicate golden brown. Remove from the oven.
The First Roll (The Warm Fusion): Let the cookies cool on the hot pan for exactly 4 to 5 minutes until they can be handled without fracturing. While still warm, drop them one by one into a shallow bowl filled with the remaining 1 cup of powdered sugar, rolling to coat entirely. Set them on a wire rack to finish cooling. Crucial: The residual heat of the warm cookie melts the initial dust layer of sugar slightly, forming a tacky, thin white icing boundary layer that permanently locks onto the cookie's exterior starch shell.
The Second Roll (The Snow Blanket): Once the cookies are completely cold to the touch (about 30 minutes later), roll them in the powdered sugar a second time. This final layer sticks to the cooled, tacky baseline, creating a thick, bright white, shatter-dry snowball aesthetic that won't absorb moisture or disappear during storage.