Position a rack in the upper third of the oven. Preheat the oven to 350°F. Grease cookie sheets.

Toast, stirring occasionally, in a baking pan until lightly browned, 5 to 8 minutes:

Set aside to cool completely, then grind until very finely chopped but not powdery or oily. Beat on medium speed until very fluffy and well blended:

Gradually beat the pecans into the butter mixture. Sift over the top and stir in until well blended:

Pull off pieces of the dough and roll between your palms into generous 1-inch balls. Space about 1-1/4 inches apart on the sheets. Bake, 1 sheet at a time, until the cookies are faintly tinged with brown, 12 to 15 minutes; rotate the sheet halfway through baking for even browning. Remove the sheet to a rack and let stand until the cookies firm slightly. Transfer the cookies to racks to cool completely. Roll the cookies until coated all over powdered sugar.