Preheat the oven to 350. Cover the bottom of a (9in) round baking pan with wax paper, and cover with butter and sugar the sides (or the whole thing instead of using wax paper. You can buy pre-cut wax paper bases in specialized kitchen stores).
Melt the chocolate, for instance by placing it in a warm place, or in the microwave. In the microwave, be very careful not to burn it, it is very easy to burn chocolate if you cook it even a few seconds too long. In a big bowl, put the yolks and a little of the sugar, and mix with an electric mixer until very fluffy and multiplied in volume, perhaps 10 minutes, depending on your mixer. Grind the nuts with most of the remaining sugar in a food processor. (Note: you can buy hazelnuts without skin, though they are more expensive. Hazelnuts with the skin are perfectly fine, you don't have to take it off, which is complicated.) Then, incorporate the nuts and the melted chocolate into the yolk, without mixing too much.
In another big bowl and with clean blades, mix the egg whites with the cream of tartar and the remaining sugar. Mix for a long time, until hard peaks form.
Now you need to incorporate the yolk batter into the egg whites. One way to do so is to start putting a couple of big spoons of the whipped whites into the mixture, to lighten it a little bit. Then add the rest of the whites, and incoporate by bringing the bottom the mixture to the top and turning. Do not use the mixer, and do not overmix. You should not deflate the mixture. It is also not necessary that the mixture be perfectly smooth. In any case, since this is not a sponge cake, even if the mixture deflates, you are going to get a harder thing, more like a brownie top, which is perfectly fine (you are not going to get brownie-like gooeyness though, since there is no added fat).
Pour the mixture into the baking pan and bake for 40 minutes or so, until a tootpick inserted into the cake comes out clean. Remove from the pan when done and let cool on a rack. Keep covered in plastic, as the cake will dry if left uncovered in a dry place.
The original recipe had butter and flour as well, plus a chocolate filling. I like the cake done in the way described. If you prefer a moister product (or even a brownie-like gooeyness), add one stick (8 tbsp) melted butter to the yolk mixture with the chocolate. Of course, the cake won't rise as much as it does without extra fat. If you like to add a filling and cover, you can do a ganache (melt 8 ounces baking chocolate with 1 cup heavy cream), or even a walnut-chocolate ganache (The easiest way is to use Nutella spread and heavy whipping cream. Whip 1 cup heavy cream and incorporate the Nutella, as much as desired. Be careful that this ganache needs to be kept relatively cold or it can melt.)