*Line 2 light-colored 9-inch round cake pans with parchment paper; grease parchment but not pan sides.
*Process hazelnuts in food processor until finely ground, about 30 seconds.
*Whisk flour, sugar, baking powder, salt, and ground hazelnuts together in large bowl.
*Whisk oil, water, egg yolks, and vanilla together in separate bowl.
*Whisk egg yolk mixture into flour-nut mixture until smooth batter forms.
*Using stand mixer fitted with whisk, whip egg whites and cream of tartar on medium-low speed until foamy, about 1 minute.
*Increase speed to medium-high and whip until soft peaks form, 2 to 3 minutes.
*Gently whisk one-third of whipped egg whites into batter.
*Using rubber spatula, gently fold remaining egg whites into batter until incorporated.
*Divide batter evenly between prepared pans and gently tap pans on counter to release air bubbles. *Bake until tops are light golden brown and cakes spring back when pressed lightly in center, 25 to 28 minutes, rotating pans halfway through baking.
*Let cakes cool in pans for 15 minutes.
*Run knife around edges of pans; invert cakes onto wire rack.
*Discard parchment and let cakes cool completely, at least 1 hour.
(for the frosting)
*Using clean stand mixer fitted with whisk, whip butter and salt on medium speed until smooth, about 1 minute.
*Reduce speed to low and slowly add sugar.
*Increase speed to medium and whip until smooth, about 2 minutes, scraping down sides of bowl as needed.
*Add marshmallow crème, increase speed to medium-high, and whip until light and fluffy, 3 to 5 minutes.
*Reduce speed to low, add hazelnut liqueur, return speed to medium-high, and whip to incorporate, about 30 seconds.
(for the topping)
*Melt the white chocolate in a bowl on top of the double boiler pan.
*Mix with green tea powder and wait until the appropriate temperature.
*Spread the chocolate on the parchment paper, and wait until it is not sticky any longer.
*Shave the chocolate with a knife and make shaved chocolate.
*Transfer the shaved chocolate on parchment paper in the rimmed baking sheet, and keep it in the refrigerator until the cake is ready to be covered.
(for the assembly)
*Place 1 cake layer on cake stand.
*Spread 2 cups frosting evenly over top, right to edge of cake.
*Top with second cake layer, pressing lightly to adhere.
*Spread remaining 2 cups frosting evenly over top and sides of cake.
*Using a small piece of parchment, scoop up half of chocolate shavings and sprinkle over top of cake.
*Once top of cake is coated, scoop up remaining chocolate shavings and press gently against sides of cake to adhere, scooping and reapplying as needed. Serve.