Finely grind the hazelnuts in a food processor. In a medium bowl, whisk the hazelnuts, flour, baking powder, and salt to blend. With a hand mixer or a stand mixer fitted with the paddle attachment, beat the sugar, oil, eggs, zest, and vanilla on low speed until the sugar is moistened, about 15 seconds. Increase the speed to high and mix until well combined, about 15 seconds more (the sugar will not be dissolved at this point). Add the dry ingredients and mix on low speed until the dough has just pulled together, 30 to 60 seconds.
Divide the dough in half. Pile one half of the dough onto a piece of parchment. Using the parchment to help shape the dough, form it into a log 11 inches long and 2 inches in diameter. Wrap the parchment around the log and twist the ends to secure. Repeat with the remaining dough. Chill in the freezer until firm, about 1 hour.
Position racks in the upper and lower thirds of the oven and heat the oven to 350°F. Line four cookie sheets with parchment or nonstick baking liners.
Unwrap one log of dough at a time and cut the dough into 1/4-inch slices; set them 1 inch apart on the prepared sheets. Bake two sheets at a time until light golden on the bottoms and around the edges, about 10 minutes, rotating and swapping the sheets halfway through for even baking. Let cool completely on racks. The cookies will keep in an airtight container at room temperature for up to 1 week.
The unbaked logs of dough may be frozen for up to 1 month.