Preheat the oven to 375 degrees F. Butter a 10-inch springform pan and set it aside. Set aside 1 teaspoon of the egg yolks for glazing.
In the bowl of a food processor, combine the remaining egg yolks, butter, and sugar and process until smooth. Sift the flour onto a piece of waxed paper and transfer to the processor. Process until just thoroughly combined. Scrape down the sides of the bowl as necessary to promote even mixing. The mixture will be sticky - use a spatula to help if necessary.
Transfer the dough to the prepared springform pan and smooth the top. Brush the top of the dough with the reserved egg yolk (add a 1/4 teaspoon of water to the yolk to help in spreading) and then use the tines of a fork to form a lattice pattern on the top of the dough. Bake for 20 minutes, reduce the heat to 350 and continue cooking until the cake is cooked through, golden, and firm to the touch, about 25 to 30 minutes longer. (If the top of the cake begins to brown too much before the cooking time is up, lightly cover with a piece of aluminum foil.) Transfer to a cooling rack until thoroughly cooled, then carefully unmold onto a plate. Serve small slices for each guest - as is, or with fresh berries if desired. This cake is very rich, so a small portion goes a long way.
Note: This cake needs to cook for 10 to 15 minutes after a toothpick inserted in the center comes out clean.