Whisk the yolks and ¼ cup of sugar, plus 1 tablespoon, in a heat safe bowl. Set over a double boiler of simmering water, stirring continuously, until an instant thermometer reaches 160 degrees. Cool. You can also choose to skip this step if using pasteurized eggs.
Beat the egg yolks and sugar in a stand mixer or with a hand held mixer until light colored and fluffy. Beat in the mascarpone cheese until smooth, scraping down the sides of the bowl often. If using a stand mixer, spoon into another bowl. Wash and dry the stand mixer bowl.
If using pasteurized eggs: Add the egg whites. Gradually shake in the ¼ cup of sugar, and cream of tartar. Beat until soft peaks form, about 3-5 minutes. Add the vanilla, but don't overmix. If using non-pasteurized eggs: Whisk the egg whites and the ¼ cup sugar in a heatproof bowl. Set over a double boiler of simmering water. Whisk quickly and continuously until an instant thermometer reads 160 degrees. Remove from the heat. Pour into the stand mixer bowl and beat on medium high to cool the egg whites. Add the cream of tartar. Beat for 3-5 minutes until soft peaks form. Add the vanilla, but don't overmix. Fold the beaten egg whites into the cream mixture.
Stir together the espresso or coffee and rum together in a flat bowl.
Clean the bowl of the stand mixer again and whisk attachment and completely dry. Whip the cream until lines begin to form from the beater. Add the sugar and vanilla and beat until fluffy. Set aside.
Using a 9x12" casserole dish, quickly dip a ladyfinger in espresso rum mixture then set in dish. Dip half of the ladyfingers quickly. Add half of the mascarpone cream. Add another layer of dipped ladyfingers, followed by another layer of mascarpone cream.
Spread the whipped cream on top. Dust with unsweetened cocoa powder and top with chocolate shavings. Cover with cellophane and refrigerate 6-8 hours or overnight before serving.
Slice into rectangular or square pieces just before serving. Will keep in the refrigerator for 1-2 days. Can be frozen in individual pieces wrapped in cellophane or parchment. Seal in an airtight container for up to 2 weeks for best flavor. Serve slightly frozen or thaw in the refrigerator prior to serving.