Grind pecans with brown sugar in a food processor until fine. Transfer to a medium bowl.
In a second bowl, use a whisk attachment to beat egg whites to stiff peaks. Add vanilla extract at the end, then gently stir egg-white mixture into nut/sugar mixture. It will be a thick paste consistency.
Drop dough by rounded tablespoon onto parchment sheets about 1-1/2 inches apart. This is the size & shape they'll remain, so drop accordingly! Dust with confectioners’ sugar, and let stand at room temperature to dry for 2 hours.
Place oven rack in center, and preheat oven to 300 degrees.
Slide a parchment sheet of cookies onto baking pan, then into oven; bake until edges are slightly darker and cookies are firm, 20 to 25 minutes.
Transfer cookies, parchment & all, to a wire rack to cool. Dust with more confectioners' sugar.