Place the flour, cooled roasted and peeled hazelnuts, and orange zest in the bowl of a food processor. Process until the hazelnuts are finely ground. Set aside.
Using a stand mixer fitted with the paddle attachment or a hand mixer, cream the butter and sugar together until light and fluffy. Scrape down the sides of the bowl, then add the eggs, one at a time, beating well to incorporate before adding the next. With the mixer on low speed, add the flour and hazelnut mixture and the milk in two additions, ending with the milk. Once the ingredients are fully incorporated, beat on medium-high speed for a few seconds.
Transfer the cake batter to the prepared baking pan. Bake for about 45 minutes, or until the Italian hazelnut cake is golden brown, puffed up, and a toothpick inserted in the center of the cake comes out with a few crumbs attached to it. Transfer to a rack and let cool to room temperature (the cake will deflate to an almost perfect flat shape as it cools down). Remove from the pan and carefully peel off the parchment paper from the bottom of the cake.
STORAGE: Store this Italian hazelnut cake under a cake dome for up to 3 days. You can also wrap it tightly in plastic wrap and refrigerate for up to 1 week, or freeze for up to 1 month.
HOW TO ROAST AND PEEL HAZELNUTS: Spread raw hazelnuts over a baking sheet and bake at 350°F (170°C) for 15 minutes, giving the tray a good shake every five minutes. When the skin of the hazelnuts is shiny and crackled, remove from the oven and transfer to a clean dish towel. Close the towel up into a bundle and rub the hazelnuts against one another vigorously to remove the skin. Open the towel and pick up the peeled hazelnuts. Some bits of skin will remain and that’s ok, simply make sure to discard all the loose papery bits. Refrigerate the roasted and peeled hazelnuts in an airtight container until needed.
FLAVOR SUBSTITUTION IDEAS: Try replacing the orange zest by one of the following options.
1 tbsp (15 ml) finely grated lemon zest, OR
1/4 cup (60 ml) cooled espresso, mixed into the wet ingredients after the eggs, OR