In the bowl of a stand mixer fitted with the whisk attachment, beat the cream on medium-high speed until stiff peaks form; transfer to a small bowl and refrigerate.
In the cleaned bowl of the stand mixer fitted with the cleaned whisk attachment, beat the egg whites on high speed until soft peaks form. Add 1 tablespoon sugar and beat until stiff peaks form; transfer to a small bowl.
In the cleaned bowl of the stand mixer fitted with the cleaned whisk attachment, beat together the egg yolks and the remaining 1/3 cup sugar on high speed until thickened and pale yellow. Gently fold the mascarpone, pumpkin puree, pumpkin pie spice and a third of the whipped cream into the egg yolk mixture. Gently fold in the whipped egg whites and refrigerate.
Place the espresso in a shallow plate. Dip both sides of the ladyfingers into the espresso and arrange in a 9-inch pie dish to completely line the bottom. Top with half of the pumpkin mixture, more espresso-dipped ladyfingers and the remaining pumpkin mixture. Top the pie with the remaining whipped cream and chocolate shavings. Refrigerate 8 hours or up to overnight, until ready to serve.