Pipe lady fingers a half inch thick only, as they puff significantly while baking.
Draw three 8 1/2-inch circles and four rows 3 1/2 inches wide on parchment paper; place on baking trays; set aside. Prepare a large pastry bag with a 1/2-inch tip, and set aside.
Heat oven to 350 degrees. Using an electric mixer fitted with the whisk attachment, whisk the yolks and 11 tablespoons sugar on high speed until mixture is thick and pale, 1 to 2 minutes. Add the flour, and fold in gently; set aside. Using the electric mixer, whisk the egg whites until frothy. While whisking, gradually add the remaining tablespoon sugar; beat until stiff, 1 to 2 minutes. Fold 1/3 of the whites into the reserved yolk mixture to lighten, then fold in the remaining whites until just incorporated.
Using an offset spatula, spread batter evenly inside the circle guides, making circles 1/4 inch thick. Bake in the oven, rotating trays once, until light golden, about 15 minutes. Transfer to wire racks to cool. While cake rounds are baking, fill pastry bag with remaining batter, and pipe ladyfingers, 1/2 inch thick, between the lines drawn on the parchment paper. Sprinkle ladyfingers generously with confectioners' sugar, and allow the sugar to soak in, about 3 minutes. Place in the oven, and bake, rotating trays once, until light golden, 15 to 18 minutes. Transfer to wire racks to cool. Once cake rounds and ladyfingers are cool, remove from parchment paper.