Place cardamom, clove, ground ginger, cinnamon, pepper, and nutmeg in a small bowl and stir together to mix well. Set aside until ready to use.

Combine milk, heavy cream, 1/2 cup sugar, fresh ginger, vanilla bean and scraped seeds, and salt in a small saucepot. Whisk to combine and bring to a simmer. Reduce heat and cook until the sugar has dissolved. Remove from heat, remove ginger and vanilla bean (save for another use, if desired), then add pumpkin puree and spices and whisk to combine.

In a separate bowl, combine egg yolks, remaining 1/4 cup sugar, and cornstarch and whisk well. Pour about 1 cup hot pumpkin mixture, 1/2 cup at a time, into eggs, whisking to combine. Pour egg mixture into remaining hot pumpkin mixture and bring to a boil while constantly stirring with a whisk. Immediately decrease heat to low and continue to cook, constantly stirring, until pudding thickens, 3 to 4 minutes. Remove from heat and strain through a sieve into a clean bowl. Place a piece of plastic wrap directly onto surface of pudding and refrigerate until thoroughly chilled, 2 hours or up to overnight.

Divide pudding into serving cups and top with whipped cream and mint leaves. Garnish each serving with two lady fingers and serve immediately.