There are lots of different names for these cookies: snowball cookies, snowdrops, tea balls, Russian tea cakes, polvorones, pecan sandies, and Mexican/Italian/Greek wedding cookies, among others. Our only family that is multiple generations old used the name butterballs, so I picked that for the family website.
This is a flexible recipe. Different versions of this cookie have quite different ratios of ingredients. For 1 cup of butter, the volume of nuts can range from 3/4 cup to 2 cups, and the volume of flour can range from 1 cup to 2 1/4 cups.
Moreover, some versions of this cookie include a bit of baking powder or almond extract. The nuts used can be pecans, walnuts, hazelnuts, a mix of those, or something else. Our old 1963 Betty Crocker's Cooky Book even has a version with an egg white—something we double down on to help keep our gluten-free version from turning into puddles.
Our original family recipe used margarine but we changed that back to butter.
Some people toast the chopped nuts to strengthen that flavor, but we do not.
Preheat oven to 350 degrees.
Set on the counter to reach room temperature:
(You can rush the temperature rise by microwaving for 15 seconds, a delay, and then microwaving for another 15 seconds.)
Chop:
Set aside the chopped nuts for now.
Separate:
Set aside the egg whites for now.
With a hand mixer, in a large mixing bowl, beat on a slow speed:
Once it becomes uniform and forms peaks, add:
Start slow to avoid making a mess. Increase the hand mixer speed when you can. Stir by hand, or knead, if needed. The mixture will eventually look and feel like buttery frosting.
Finally, stir in by hand:
Knead by hand if necessary. Adjust the amount of flour in this step so that the dough becomes not only firm but just barely crumbly.
If you care about having cookies with a very round shape, refrigerate the dough for several hours. This will prevent the cookies from having flat bottoms after baking.
Put a silpat on a cookie sheet. We like bite-size cookies and use a 1 Tablespoon scoop to measure out lumps of refrigerated dough. Smooth out each surface to make them rounder, or the coating of powdered sugar will thickly fill in the cracks like rivers forming in valleys.
Bake for 12 minutes. The cookies will not brown. While they bake, prepare:
Roll the cookies in the powdered sugar as soon as they are cool enough to touch (perhaps only a minute of cooling). This will make a thicker and slightly melted layer.
(If want to freeze the cookies, do so now and save the final step until later.)
After the cookies have finished cooling, roll them in the powdered sugar a second time so they gain their traditional snowball appearance.