In a medium saucepan over medium heat, whisk together the heavy cream, whole milk, and pumpkin puree. Heat until mixture begins to steam and bubbles form around the edges. 

In a separate bowl, whisk together the egg yolks and brown sugar until well combined. 

Very, very slowly pour about half of the warmed pumpkin mixture into the egg yolk mixture while whisking constantly. This process will "temper" the eggs, so they don't "scramble" from the heat of the warmed pumpkin mixture.

Pour the tempered egg yolk mixture back into the saucepan with the rest of the warmed pumpkin mixture, and whisk to combine and create the custard mixture.

Cook the custard mixture over medium heat, stirring constantly, until it thickens and coats the back of a wooden spoon, about 5-7 minutes. Turn heat down just a bit if the mixture gets too hot. 

Pour the custard through a fine mesh sieve into a heatproof bowl, to remove any little pieces of egg or pumpkin from the ice cream. Then stir in the vanilla and pumpkin pie spice. 

Place plastic wrap directly onto the surface of the custard, to prevent it from forming a skin. Chill the ice cream base in the fridge until very cold - at least 4 hours, but preferably overnight. To speed up this step, you could place the bowl in the freezer instead, stirring every 20 minutes until thoroughly chilled.

Once chilled, pour the custard into an ice cream maker bowl (make sure it's thoroughly frozen) and churn according to the manufacturer's instructions, until the mixture reaches a soft-serve consistency. This usually takes 15-20 minutes or so.

Enjoy right away, with its soft-serve consistency. Or transfer the soft-serve ice cream to a loaf pan and wrap it tightly in plastic wrap. Freeze for an additional 4 hours or until firm and scoopable. Enjoy!