In a large bowl, combine the butter, flour, sugar, baking powder, and salt. Use a pastry cutter or 2 dinner knives to cut in the butter until the mixture is fine and crumbly. In a small bowl, beat 2 of the eggs and the vanilla together and stir into the dry ingredients. Mix the dough just until all the ingredients come together. Turn the mixture out onto a floured work surface and knead for a minute or two by hand to form a cohesive dough. It should be somewhat sticky. Wrap the dough in plastic wrap and refrigerate for 1 hour.

Preheat the oven to 350°F. Line 2 baking sheets with parchment paper. Spread the walnuts out on a piece of waxed paper.

Dust your hands with flour and shape the dough into 3 ropes, each about 1½ inches in diameter. Cut each into 2-inch pieces. In a small bowl, beat the remaining egg. Dip each of the pieces into the beaten egg, then roll in the walnuts to coat evenly. Place the cookies about 1½ inches apart on the prepared baking sheet.

Bake the cookies until they are lightly colored, 12 to 15 minutes. Slip the parchment, with the cookies, off each baking sheet and let cool on wire racks. Let stand for 2 minutes before peeling the cookies off.

Variation: Dust the cookies with confectioners’ sugar before serving.