Preheat oven to 350°F. Line 3 baking sheets with parchment paper. Trace 8x8 inch squares on each sheet as guides.

Separate 6 eggs. Beat yolks with 1/4 cup sugar until pale and thick, about 5 minutes. Set aside.

In clean bowl, whip egg whites until soft peaks form. Gradually add remaining 1/2 cup sugar. Beat until stiff, glossy peaks appear. Fold in vanilla.

Gently stir yolk mixture into whites. Sift flour and salt together. Fold into egg mixture in 3 batches, being careful not to deflate.

Transfer to piping bag with large round tip. Pipe 4-inch strips onto prepared sheets, 1 inch apart. Dust generously with powdered sugar.

Bake for 10-12 minutes until golden. Cool completely on wire racks. Lady fingers will crisp as they cool.

For custard: whisk 6 egg yolks, milk, and 1/2 cup sugar in saucepan. Cook over medium heat, whisking constantly, until mixture boils. Boil 1 minute. Cool gradually, whisking occasionally. Refrigerate 1 hour.

Beat heavy cream and powdered sugar until stiff peaks form. Set aside.

Beat mascarpone and vanilla until smooth. Add chilled custard. Beat until combined. Gently fold in whipped cream.

Combine coffee and rum in shallow dish. Quickly dip each lady finger 1-2 seconds per side. Arrange in single layer in 8x8 dish.

Spread 1/3 of cream mixture over lady fingers. Repeat with 2 more layers of dipped lady fingers and cream.

Dust top with cocoa powder. Cover and refrigerate at least 24 hours before serving for best flavor.