Preheat the oven to 350° F (180° C) and spray two 9-inch cake pans with nonstick spray. In a medium bowl, combine the spent grain flour, ground hazelnuts, baking powder, and salt. Stir until fully combined.
In a large bowl, with an electric mixer fitted with a whisk attachment, beat the egg whites on high speed until soft peaks form. Continue to mix, adding the 1/4 cup sugar a little at a time, until the egg whites form stiff peaks. Store the whipped egg whites in the refrigerator until ready to add.
In a large bowl, with an electric mixer fitted with a whisk attachment, beat the egg yolks and 3/4 cup sugar on high until the mixture is pale yellow and has a pudding-like consistency, about 1-3 minutes. On low speed, mix in the hazelnut liqueur or vanilla extract and the milk.
Switch to a baking spatula and sprinkle half the flour mixture over the batter, stirring with the spatula until just combined. Repeat with the second half of the flour. Add half of the whipped egg whites, folding them into the batter with the spatula until just combined. Repeat with the second half of the egg whites, folding until there are no more white streaks, but being careful not to overmix.
Pour the batter into the prepared cake pans and bake at 350° F (180° C) for about 22-25 minutes, or until the cakes are lightly browned on top and spring back a little to the touch. Allow the cakes to cool for at least 45 minutes before assembly.