Separate eggs. Discard whites. In the bowl of a stand mixer, whip yolks and sugar until it turns a light yellow color, about 3 minutes. Incorporate pumpkin and whip until smooth.
Meanwhile, heat milk, half-and-half, and spices over medium-low heat, stirring constantly. When milk begins to steam, but not boil, remove from heat and temper the egg mixture by adding 1/2c of the hot milk to the eggs and whisking together. Then, pour egg mixture into milk mixture and whisk briskly until combined. Return to heat, whisking constantly, until it begins to thicken slightly, just when it starts to simmer. Remove from heat.
Add extracts and strain into a pitcher to remove whole spices. Chill in refrigerator until ready to serve. If, after chilling, eggnog is too thick, thin gradually with milk until preferred consistency is achieved.