Preheat the oven to 400 F and line 2 baking trays with parchment paper.
Sift the flour and cornstarch together and set aside. Whip the egg yolks with 3 Tbsp of the sugar until thick and pale and they hold a ribbon when the beaters are lifted. In a separate bowl, whip the egg whites with the cream of tartar until foamy, then slowly add the remaining 6 Tbsp of sugar and continue whipping until the whites hold a medium peak when the beaters are lifted.
Fold the whites into the yolk mixtures using a whisk, then fold in the flour until just incorporated. Fill a piping bag fitted with a large plain tip and pipe lady fingers onto the prepared trays that are 4-inches long and an inch apart (they will spread a little once piped). Bake for about 8 minutes, until the fingers are an even golden brown. Allow the fingers to cool completely before removing them from the trays.
For dipping, melt the chocolate in a metal bowl place over a pot of barely simmering water and stirring until smooth. Dip each ladyfinger a third into the chocolate and place on a clean parchment-lined baking trays to set (chill for a little, if needed).
The dipped ladyfingers should be enjoyed the day they are dipped, but undipped ladyfingers can be stored in an airtight container for up to 5 days.