Combine the pumpkin puree, brown sugar, and pumpkin pie spice in a small pot and heat over medium heat until it boils. Stir the mixture constantly. Lower the heat to medium-low and cook for 5 minutes while continuing to stir. Remove from the heat and set aside.
In a medium pot over medium heat, combine the milk, heavy cream, and 98 grams of sugar. Bring the mixture to a simmer. Meanwhile, whisk the remaining sugar, egg yolks, and cornstarch together in a medium bowl until light.
Once the milk has reached a simmer, pour a small amount of it into the bowl of egg yolks, sugar, and cornstarch. Whisk together while continuing to pour a steady stream of warm milk. Pour the yolk mixture back into the pot and heat over medium heat. Add the spiced pumpkin puree.
Bring the pastry cream to a boil while whisking continuously. Boil for 1-2 minutes.
Pour the pumpkin pastry cream through a mesh strainer into a bowl with the butter and vanilla bean paste. Stir the pastry cream until the butter is melted and fully combined.
Apply plastic wrap to the top of the pastry cream to prevent a crust from forming and chill until ready to use.
Whip the heavy cream to stiff peaks and fold into the cold pastry cream.