For the ice cream base, in a medium saucepan, combine heavy cream, milk, ¼ cup sugar, and salt. If using vanilla bean, scrape the seeds into the mixture and add the pod. If using paste or extract, add to the mixture. Cook over medium heat. Bring mixture just to a simmer, about 5 minutes, stirring often until sugar has dissolved. Remove from heat.
In a large bowl, whisk egg yolks and 3 tablespoons sugar until pale, about 2 minutes. While whisking, slowly pour 1/3 of hot cream into the yolks. Then whisk the yolk mixture back into the pot with the cream. Return the pot over medium heat and cook until the mixture is thick enough to coat the back of a wooden spoon (about 170˚F on an instant thermometer), about 3 minutes, stirring constantly.
Strain the custard into a medium bowl. Cool mixture to room temperature. Transfer to an airtight container and chill in the fridge for at least 4 hours.
For the apple filling, in a medium pot, combine apple cubes, brown sugar, butter, cinnamon, all spice & salt. Cook over medium heat until the apples are soft but still hold their shapes, about 12 – 15 minutes, stirring occasionally. Remove from heat and let them cool to room temperature. Transfer to an airtight container and chill in the fridge for at least 1½ hours.
For the pie crust bites, in a large bowl, whisk together flour and salt. Add butter. Using a pastry cutter or your fingers to cut the butter into the flour until the mixture looks crumbly and the largest pieces of butter are pea-sized. Add 2 teaspoons ice water and stir. Squeeze the mixture together to make a dough. If needed, add ½ teaspoon of ice water. Shape the dough into a disk and wrap in plastic wrap. Keep in the fridge for at least 30 minutes or up to 24 hours.
Preheat the oven to 400˚F (200˚C). Line a parchment paper on a baking sheet.
Take out the dough and cut into 8 parts. It doesn’t have to be evenly divided. Roll each part into a long stripe with about 1/3-inch diameter. Transfer to another baking sheet. Repeat with the rest of the dough. Transfer to the baking sheet with the dough to the fridge and chill for 10 minutes.
In a medium plate, pour in the sugar. Set aside.
When the dough is chilled, cut them into ¼-inch bites. Roll them in the sugar and put on the prepared baking sheet, leaving spaces in between. Don't worry about sugar getting onto the baking sheet. Just leave them there. Bake in the oven for 14 – 16 minutes or until golden brown. Transfer to a plate lined with paper towels. Cool completely at room temperature. Transfer to the freezer to harden for 1 hour before churning.
When everything is ready, pour the ice cream base into the ice cream machine and follow the machine instruction. Once the ice cream is ready, add the apple filling little by little. Add some and churn. Add more and churn, until you are happy with the amount of apple in the ice cream. Stir in a desired amount of pie crust bites with a wooden spoon. Transfer the ice cream to an airtight container. Freeze until firm, at least 4 hours.
Let the ice cream sit at room temperature for 10 - 15 minutes before scooping. Serve and enjoy.