Preheat oven to 325°F. Line a baking sheet with parchment paper.
Pulse toasted pecans with 2 tablespoons confectioners sugar in a food processor until finely ground.
Whisk together flour, salt, and baking powder in a bowl.
Beat together butter, remaining 2/3 cup confectioners sugar, and vanilla in a bowl with an electric mixer at high speed until pale and fluffy, about 3 minutes. Add egg yolk (reserve the white) and beat well. Add flour and ground-pecan mixture and mix at low speed until just combined, 30 seconds to 1 minute. (Dough will be crumbly but will hold together when squeezed.)
Halve dough and roll out 1 half between 2 sheets of wax paper until 1/4 inch thick (about a 9-inch round). Cut out as many rounds as possible with a cookie cutter and arrange about 2 inches apart on baking sheet. Roll out scraps and cut remaining dough in same manner.
Beat egg white until frothy, then brush tops of rounds lightly with egg white. Put a pecan half on top of each round, then brush pecan lightly with egg white.
Bake cookies in middle of oven until tops are pale golden, 15 to 20 minutes. Cool cookies on sheets on racks 2 minutes, then transfer to racks to cool completely.