To make the cookies: To the bowl of a stand-up mixer, add the butter, sugar and salt. Beat until light and fluffy, about 3 minutes. Add the egg, egg yolk, vanilla extract and beat once more until combined. In two batches, add the flour, being sure each addition is combined before adding the next one. Divide the dough in half, transfer it to two sheets of plastic wrap (it’ll be quite soft!), shape into a disc and transfer to the fridge. Allow to chill for about 1 hour. Ideally it should be at least 3 hours.
To make the hazelnut chocolate butter: Preheat the oven to 350 degrees F. Spread the hazelnuts onto a baking sheet. Roast for 7 to 10 minutes, until the skins turn a darker shade of brown. Immediately place the skins in the center of a clean kitchen towel. Wrap up the hazelnuts and rub them back and forth until all the skins fall off. Some skins may not come off—that’s ok! If any are really stubborn, you can transfer those hazelnuts back to the oven to roast for an additional 5 minutes. Again, rub them in the kitchen towel until most of the skins have fallen off.
Transfer the hazelnuts, one cup at a time, to the Vitamix 40-ounce container. Start machine and slowly increase to its highest speed. Remove the lid plug and use the tamper to press the hazelnuts into the blades while blending. Process until hazelnut butter is very smooth, about 2 to 3 minutes.
Pour in the oil, powdered sugar, cocoa powder and salt. Pulse once more until very smooth, about 30 seconds. Transfer to a jar.
Turn the oven up to 375 degrees F. Line two baking sheets with parchment paper and set aside.
Remove the first disc of dough from the fridge. Allow to come to room temperature for about 10 minutes. Liberally flour a rolling pin and work surface. Roll out the cookie dough to a 1/8-inch thickness. Stamp out the cookies with a cookie cutter of your choice. Transfer the cookies to the baking sheet, spacing them about 1-inch apart (these spread slightly). To half of the cookies, take the tip of a piping tip and stamp out the center. Re-roll the scraps to get a few more cookies. Repeat with the second disc of dough.
Bake the cookies, one baking sheet at a time, for about 8 to 10 minutes, until lightly golden brown around the edges. Cool on the baking sheet before transferring to a cooling rack. Repeat with the remaining cookies.
Transfer the cookies tops (the ones with the center hole removed) to a cooling rack. Dust with a liberal amount of powdered sugar. Flip the cookie bottoms (the ones without the center hole removed) over and smother a scant teaspoon of hazelnut butter onto the cookie. Repeat with the remaining cookies. Place the tops on the bottoms and sandwich the two together. Cookies will last 3 days when kept in an airtight container.