Ice Cream Base. Fill a large bowl half-way with ice. Pour cold water over the ice, filling the bowl no more than two-thirds high. Place a clean bowl on top of the water bath. Place a strainer over the empty bowl.
Combine the milk and heavy cream in a large measuring cup or a bowl. Set aside.
Boil syrup in a 3 or 4-quart saucepan over moderately high heat until reduced to approximately 3/4 cup (242 g.), 5 to 10 minutes. To keep it from burning, stir it frequently. (For deeper flavor, take it to the caramel stage by cooking until the syrup is thick, stirring constantly.) Carefully whisk in the milk and cream. (It will bubble up initially). Add salt and bring to a boil over medium heat. (If your syrup caramelized, it will likely seize up and harden when you add the milk and cream. Do not panic! Keep heating it up and stirring constantly. The caramel will liquify as the mixture heats up again.) Continue heating until the mixture comes to a simmer.
When you first turn the heat on for the syrup, vigorously whisk the egg yolks in a medium size bowl to aerate them as much as possible.
Once the liquid mixture comes to a simmer, turn the heat off and let it sit for a minute or two. With the bowl holding the egg yolks secured on the counter (if no one is around to hold it, place it on a rubber mat or wrap a wet around the base of the bowl), slowly pour half the heated liquid mixture into the yolks, whisking constantly. Once fully incorporated, pour the contents of the bowl back into the saucepan. Over a medium-low heat, stir the mixture constantly with a wooden spoon until it reaches 185°F or a line holds when you drag your finger across the back of the wooden spoon. (It should only take a minute or two to reach the correct temperature.)
Pour custard through the strainer into the clean metal bowl on top of the ice bath. Stir occasionally. After 10-15 minutes, the mixture should be at room temperature. Place plastic wrap on top of (literally touching) the ice cream base and chill in the refrigerator at least 4 hours and preferably overnight.
Pie Crust. In a mixing bowl, whisk together the flour, sugar and salt. Add all the butter. Using your hands, coat each piece of butter with the flour mixture. Pinch the pieces of butter to flatten them a bit. Keep working the mixture for a couple of minutes until the mixture resembles coarse sand with most of the clumps of butter the size of peas and some larger pieces the size of walnuts. Make a well in the middle. Add 1 tbsp. of ice cold water. Using your hands, scoop the flour from the sides and the bottoms to hydrate the flour with the water. If the mixture is too dry, create another well in the middle and add an additional 1/2 tbsp. of ice cold water. Repeat if necessary. You know you are done when a clump of dough flattened in your palm is smooth. Pour the entire mixture onto a sheet of plastic wrap. Push down on the plastic wrap to flatten the dough together into a rectangle. Refrigerate at least 30 minutes.
Roll dough out to a rectangle. You are not looking for perfection here. The important thing is to roll it out to approximately 1/8 of an inch. Place in freezer for 15 minutes or refrigerator for 30 minutes.
Preheat oven to 400°F. Place a piece of parchment paper over the top of the dough and a baking sheet on top of the parchment paper. Place in oven and bake for 16-17 minutes, until the sides of the dough are browned. (You will have to pull off the top baking sheet and parchment to check on the dough.) Remove the top baking sheet and parchment sheet and continue baking 4-5 minutes. Remove from oven and allow to cool completely.
Blueberry Pie Filling. Combine all ingredients in a small saucepan and bring to a boil over medium heat, stirring with a wooden spoon and crushing the blueberries as it cooks. Cook approximately 5 minutes until the blueberries are soft and the mixture is thick and deep blue in color. Allow to cool to room temperature. Spread on prepared pie crust.
Churning and assembly. Freeze custard in ice-cream maker following the manufacturer’s instructions. In the meantime, cut the prepared “blueberry pie” into small pieces, approximately ¼ of an inch squares. Once the ice cream is done churning, add the blueberry pie pieces and churn until fully combined. (Alternatively, fold in blueberry pie pieces with a rubber spatula.) Transfer to an airtight container and cover with a piece of parchment paper or plastic wrap directly on the surface. Cover container and freeze.