Using stand mixer with whisk attachment, beat egg yolks and sugar until thick, about 5 minutes. Add room temperature mascarpone and continue to beat until smooth. Add 1 Tbsp espresso and 1 Tbsp balsamic and mix until thoroughly combined.
In shallow bowl, mix remaining espresso and balsamic. Briefly dip each ladyfinger into espresso mixture. (Allowing ladyfingers to soak too long will cause them to fall apart.) Place ladyfingers on bottom of 13" x 9" baking dish, breaking in half if needed to fit bottom. Evenly spread 1/2 mascarpone mixture over ladyfingers. Arrange another layer of soaked ladyfingers and top with remaining mascarpone mixture. Cover with plastic wrap and refrigerate at least two hours or up to six.
Before serving, sprinkle top with chocolate shavings.