Preheat oven to 350 F/177 C. Grease and flour two cookie sheets or line them with parchment.
Pour flour, sugar, salt, and baking powder into the bowl of your mixer, then add the vanilla and eggs. Run mixer until the dough starts to form. Add nuts, and continue to mix for a few minutes until the dough forms a ball on the paddle. (If dough is too sticky, add more flour as needed.)
Divide the dough into four equal parts, then roll each part into a log about 2" wide and 1" high. Place two on each cookie sheet, at least two inches apart.
Beat the last egg and brush it on top of the logs.
Bake at 350 F/177 C for 30-35 minutes, until the logs are golden. Take them out of the oven and reduce the temperature to 325 F/160 C.
When the logs are cool enough to handle (about 5 minutes), slice them diagonally with a serrated knife. Place the slices back on the cookie sheets, laid on their sides, and bake for another 10-15 minutes.
Cool completely, and store in an airtight container.