1/2 cup bourbon, for serving
For the ice cream base: In a large saucepan, bring the half-and-half and 1/2 cup sugar to a boil.
Whisk the yolks with the remaining 1/2 cup sugar. Pour some of the hot cream into the yolks to gently heat. Add the yolks to the half-and-half and cook gently over medium heat until the mixture reaches 120 degrees F, 2 to 3 minutes. Divide in half.
For the pumpkin ice cream: Whisk together the pumpkin, cinnamon, ginger and nutmeg. Add 2 cups ice cream base. Puree with a hand blender. Let sit in the refrigerator overnight, or at least a few hours to "ripen."
For the eggnog ice cream: Blend 2 cups ice cream base, nutmeg and bourbon with a hand blender. Let sit in the refrigerator overnight, or at least a few hours to "ripen."
Churn the pumpkin ice cream first and deposit into six 4-ounce half sphere flexi molds (or line 6 ramekins with plastic wrap).
Churn the eggnog ice cream. Hollow out the center of the pumpkin ice cream with a melon baller or warm spoon. Pour the semi-frozen eggnog ice cream into the cavity and let firm overnight.
For the gingerbread cake: Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper.
Sift together the flour, baking powder, cinnamon, salt, baking soda, ginger, cloves and nutmeg.
Cream the butter and sugars. Add the eggs one at a time.
Mix the ginger with the buttermilk. Add the dry ingredients in three installments to the creamed butter, alternating with the buttermilk mixture. Spread evenly onto the prepared baking sheet and bake until the cake bounces back when lightly pressed, about 15 minutes. Cool.
Cut the cooled cake into rounds that fit the bottom of the flexi molds or ramekins. Place on top of the ice cream and return the molds to the freezer until ready to serve.
For the meringue: Gently heat the sugar, egg whites, vanilla seeds and salt in the bowl of a stand mixer over a water bath until it is warm and the sugar dissolves. Beat with the whisk attachment on high until cool. Transfer to a piping bag.
Unmold the ice creams and cover with meringue. (Alternatively, you can spread the meringue with an offset spatula.) Brown with a kitchen torch.
To serve, heat the bourbon in the microwave in a heatproof glass. Light on fire in the glass and pour over the baked Alaska. Serve immediately.