In a medium bowl, beat egg yolks, 1/4 cup granulated sugar and vanilla on high speed until thick and pale yellow, 2 to 3 minutes. Scrape into larger bowl. Return the flour to the sifter and sift evenly over the top of the eggs. Do not mix in. (No sifter? Just distribute evenly.)
In a large clean bowl, beat the egg whites and cream of tartar to soft peaks. Increase speed to high, gradually add 1/3 cup granulated sugar, and beat until peaks are stiff.
With a spatula, fold a third of egg whites into egg yolk mixture, gently stirring until almost no streaks remain. Fold in the remaining whites in two batches, gently lifting from the bottom and folding over the top until few streaks remain, taking care not to deflate the whites.
Spoon the batter into a large pastry bag fitted with a5/8-inch plain tip. (It helps to stand the bag upright in a vase to fill it. No pastry bag? Fill a plastic bag and snip off one corner.) Pipe the batter onto the parchment paper. Each ladyfinger should be about 1 inch wide and 5 inches long. You'll need 16 to 20 ladyfingers for the charlottes, plus about a dozen more for the bases (or make discs).
To give the ladyfingers a thin veneer of crispness, here's a tip from the new "Sprinkle Bakes" by Heather Baird (Sterling, $19.95). Instead of sifting only once with powdered sugar before baking, Baird sifts half of the sugar over the ladyfingers, then waits 5 minutes until the sugar begins to melt. Sift the remaining sugar over the pastries.
Place pans on oven racks and bake for 6 minutes, then switch positions. Bake for 6 minutes more, then slide the parchment onto a wire rack to cool. Gently peel the ladyfingers from the parchment and store in an airtight container not more than a day, or use immediately.