While you could theoretically start the ice cream for this pie on Saturday morning and serve it that evening, it's better and easier to think of this as a two-day affair. Prepare the ice cream base and freeze it in the graham cracker crust on one day, and then plan on serving it the next.
It should also go without saying that you can replace the blueberry topping on this cheesecake pie with any fruit your cheesecake-loving heart desires. If your fruit is very fresh and ripe, don't even bother making it into a sauce — just slice the fruit and arrange it right on top of the pie.
Blueberry or otherwise, sauce or no-sauce, the fruit topping is best added just before serving so you get the contrast of that soft and juicy fruit with the cold and creamy ice cream.
One last thing: Astute observers will note that if you make the crust yourself, this recipe is no longer truly "no-bake." I find that making a graham cracker crust is so quick and easy that it barely heats the kitchen. But a store-bought graham cracker crust was invented for the hottest days of summer, and it is a perfectly fine option here.
Note that the graham cracker crust (if making by hand) and blueberry sauce can either be prepared ahead of time or while the ice cream base is chilling. Both need to be completely cooled to room temperature before assembling the ice cream pie.
Blueberry Cheesecake Ice Cream Pie
Make one 9-inch pie; ice cream recipe adapted from Jeni's Splendid Ice Creams
For the blueberry sauce:
2 cups (12 to 16 ounces) fresh or frozen blueberries
1/4 cup (2 ounces) brown sugar
1 lemon, zest and juice
For the ice cream:
1 cup (8 ounces) cream cheese
1 tablespoon cornstarch
2 cups (16 ounces) whole milk
1 1/4 (10 ounces) cups heavy cream
2/3 cup (5 1/3 ounces) sugar
1/4 cup (2 ounces) light corn syrup
1/8 teaspoon salt
1 medium lemon, zest and juice
1 9-inch graham cracker crust, either store-bought or homemade (baked and cooled if homemade)
Twenty-four hours before making the ice cream, place the bowl of your ice cream maker in the freezer.
For the blueberry sauce, combine the blueberries, brown sugar, lemon zest, and lemon juice in a small pan over medium-high heat. Bring to a boil, then reduce heat to medium-low. Simmer until the berries have released their juices and become syrupy, 12 to 15 minutes. Stir occasionally, but try not to mash up the berries too much. Remove from heat and allow to cool, then refrigerate at least 4 hours until completely chilled. The syrup can be made up to a week ahead.
To make the ice cream, cut the cream cheese into small pieces and place in a medium-sized bowl. Whisk together the cornstarch with 2 tablespoons of the milk in a separate ramekin and set aside.
Bring the remaining milk, cream, sugar, corn syrup, and salt to a boil in a large saucepan and continue boiling for 4 minutes. The milk will double in bulk as it bubbles, so use at least a 4-quart saucepan or larger for this step. If it looks like the milk is going to bubble over the sides, lower the heat just enough so the milk is still bubbling but no longer threatening to boil over.
Remove the saucepan from heat and whisk in the cornstarch mixture. Bring it back to a boil over medium-high heat and cook until it just starts to thicken, about 1 minute.
Add the lemon zest to the milk (reserve the juice to add once the milk is chilled; adding it to hot milk can cause curdling). Whisk the hot milk into the cream cheese in several additions, whisking between each addition to melt the cream cheese evenly. Let cool to room temperature, then chill completely in the fridge for at least two hours or overnight.
When the ice cream base has chilled, stir in the reserved lemon juice and churn it in your ice cream maker until thick, about 20 minutes (or according to your ice cream maker's instructions). Pour about half the ice cream into the cooled pie crust, filling it right up to the edge. Press a square of parchment to the surface of the pie and freeze at least 4 hours or overnight. (The remaining ice cream can be transferred to a freezer-safe container and frozen for midnight snacking.)
When ready to serve, spoon the cooled blueberry syrup over the pie and slice into wedges. Leftover pie can be frozen with the blueberry sauce on top.