Preheat oven to 350 (180° C).

If using whole hazelnuts, increase temperature to 400 and roast the nuts for 10-20 minutes, or until the skins are browned and the nuts are fragrant. The skins should rub off easily - if not, roast for another 5 minutes. Remove from the oven and let cool. Reduce oven temperature to 350.

Beat together the butter and sugar until completely incorporated (5 minutes in a stand mixer), then add the egg yolks and continue to beat until thick and pale (another 5 min). 

Meanwhile, gather the hazelnuts into a kitchen towel and rub them together with both hands to remove most of their skins (the towel will stain, so use one reserved for this purpose). Place into a food processor and grind until it resembles coarse cornmeal. Grinding too long will turn them into hazelnut butter, so don't overdo it.

Add the the ground hazelnuts to the butter mixture until just incorporated. In a separate bowl beat the eggs whites until they form stiff peaks, then fold them gently into the cake mixture.

Pour into a buttered cake pan of any desired shape and bake until a knife inserted into the middle comes out clean, about 45 minutes.

Notes:

Roasting the hazelnuts adds critical depth to the flavor of this cake. Don't skip it.