1/2 cup walnuts, lightly toasted
1 1/4 cups sugar, divided
7 large egg yolks
16 tablespoons salted butter, melted and cooled slightly
2 cups unbleached, all-purpose flour
Preheat the oven to 300 degrees F. Butter and lightly flour a 9-inch cake pan.
Place the walnuts and 2 tablespoons of the sugar in the bowl of a food processor and grind so that most of the walnuts are finely ground but not anywhere near a paste.
In a large bowl, whisk together 6 of the egg yolks and the remaining sugar until the mixture is blended, just a few minutes; there is no need to use an electric mixer here. It will be thick and yellow but shouldn’t form a ribbon. Slowly whisk in the walnuts and sugar, then the butter. Sift the flour over the mixture and whisk it in just until the mixture is homogeneous. Don’t overmix the batter or the cake will be tough.
Whisk together the remaining egg yolk and 2 teaspoons water to make an egg glaze.
Turn the batter, which will be quite stiff, into the prepared pan and smooth it out. Lightly but thoroughly paint it with the egg glaze. Using the back of the tines of a fork, deeply mark a crisscross pattern in the top of the cake, going three times across it in one direction, then three in another. (The marks in the cake will fade, leaving just their trace on the top of the cake.)
Bake in the center of the oven until the cake is deep golden on the top and springs back slowly but surely when it is touched, about 1 hour and 15 minutes. Using a knife or cake tester isn’t recommended as it always comes out looking slightly damp because of the amount of butter in the recipe.
Remove from the oven, transfer the cake to a wire tack, and let cool for about 10 minutes before turning out of the cake pan. Let it cool thoroughly before serving.