Preheat the oven to 325 F and place a rack in the middle of the oven.
Wrap the bottom of the tart with one large sheet of aluminum foil. This is to prevent any water from leaking into the tart when it bakes in the water bath.
Heat as much hot water as you can in a kettle while prepping the custard.
In a medium pot, whisk together the whole milk, heavy cream, 50 grams of the sugar, and a pinch of salt. Place over medium heat until it starts to steam.
While the milk is heating, separate the 4 eggs. Place 4 egg yolks in a medium heat safe bowl and pour in the remaining 50 grams of sugar and 3 teaspoons of pumpkin pie spice. Whisk until paler in color.
Place the bowl with the egg yolk mixture on a damp rag to prevent it from spinning.
Once the milk is steaming, remove it from the heat and slowly stream it into the egg yolk mixture while constantly whisking the egg yolks.
Continue to pour and whisk until all of the milk has been added in.
Then pour the custard mixture back into the pot.
Place the pot back on the stove and heat over low heat.
Switch to using a rubber spatula to stir the custard in a figure 8 pattern, making sure to scrape the bottom and sides of the pot as you stir.
Once the small bubbles on top of the custard start to go away, remove it from the heat immediately.
Pass 250 grams of the honeynut purée through a sieve into a medium heat safe bowl. Then pour the custard through the sieve into the same bowl and whisk to combine.