In a saucepan, heat milk, cream, and vanilla over medium until steaming.
In a bowl, whisk egg yolks, brown sugar, cinnamon, and pumpkin spice until smooth.
Slowly whisk in hot cream (one ladle at a time) to the egg yolk mixture to temper. Return the mixture back to the saucepan and cook over a medium-low heat, stirring constantly, until the custard coats the back of a spoon (170–175°F).
Remove from the heat and blend in the pumpkin puree with a hand blender until smooth. Strain the custard through a fine-mesh sieve into a bowl resting on a ice bath.
Cover and chill for at least 4 hours or overnight in the refrigerator.
Churn in an ice cream maker according the the manufacturer’s instructions. Transfer to a container, press parchment on top, and freeze 4–6 hours until firm.