Place egg yolks in a large bowl and beat using an electric blender until pale yellow, about 5 minutes. Add whipping cream and vanilla extract; mix until well combined.
Combine pumpkin puree, brown sugar, white sugar, maple syrup, evaporated milk, pumpkin pie spice, cinnamon, and salt in a saucepan over medium heat. Cook and stir until sugars are dissolved, 5 to 7 minutes. Remove from heat and let cool slightly. Stir in milk and mix until well combined.
Slowly pour pumpkin mixture into the egg mixture and stir together until well combined. Pour eggnog through a wire-mesh strainer into a container and refrigerate overnight. Pour 1 tablespoon brandy into each cup of eggnog.
