Place the flour on the counter and make a well. Cut up the butter and place the sifted sugars, butter, yolks, rum, and vanilla powder in the well. Work the well together.
Work in the flour then "fraisage" the dough, pushing it away from you on the counter with the heel of your hand. This helps schmear the butter into thin layers to make the cake flakey in the end. Chill the dough 30 minutes.
Preheat the oven to 360 degrees F.
Butter an 8-inch cake pan and line the bottom with parchment and butter the paper. Roll the dough out on a lightly floured surface to an 8-inch disk about 1/2-inch thick. Flip it over onto your hand and brush off the excess flour then place it in the pan. Brush the top with egg wash; then egg wash it again to get a thicker coating. Using a knife, decorate it with the traditional cross-hatching, or for restaurant presentation you carve a map of Brittany on the surface and do some angled lines all around the edge. Bake until golden brown, about 30 to 40 minutes. Let cool in the pan and serve in wedges.
I kept this recipe in the original metric measurements I was taught it in to show the relationship between the ingredients. Quatre-Quarts (meaning "four quarters") is a French cake shaped like a rectangle and all the ingredients (butter, sugar, flour, and eggs-oooo that would make a good book title, don't you think?) are of equal weights. My teacher, Chef Claude at La Varenne said you weigh the eggs and then match that measurement with the other ingredients.
If you look this up in the dictionary, Quarte-quarts translates to pound cake, the American version of a pound of 4 equal ingredients, but with air whipped in for leavening. This cake is dense and buttery with a big crumb, more like a shortbread than a cake.
You can do the mixing in a food processor but this recipe is the traditional way.