Whisk the instant pudding mix with the cold milk in a large bowl until it begins to thicken, about 2 minutes.
Stir in the pumpkin puree until the mixture is smooth and evenly colored.
Mix in the brown sugar, pumpkin pie spice, cinnamon, vanilla, and salt until creamy.
Cover and chill for at least 10 minutes to set and thicken.
Spoon into cups, add a dollop of whipped cream, and sprinkle with cookie crumbs if using. Serve cold.