In a medium sauce pan, combine the heavy cream, milk, 1/3 cup sugar, vanilla, and salt, and bring to a gentle simmer over medium heat. Use a wooden spoon to stir, dissolving the sugar, and bring the cream mixture to about 175 degrees (about 8 minutes).
Turn off the heat, cover the pan, and allow the vanilla infused cream to steep for 15 minutes.
Meanwhile, whisk the egg yolks in a separate bowl, and slowly add the sugar, whisking for about 4 minutes, or until the eggs are light in color and thick.
When the cream finishes steeping, ladle 1 cup of the hot cream in a drizzle into the eggs while whisking to temper. Pour the egg mixture back into the saucepan, and gently cook over medium low heat, stirring constantly with a wooden spoon for about 8-10 minutes. The custard is ready when you are able to coat the back of your wooden spoon and run your finger down, leaving a line.
Prepare an ice bath. Strain the mixture into the prepared bowl of the ice bath. Depending on your sieve, you may need to strain twice to get a nice, smooth consistency.
Let the ice cream custard cool for 1 hour in the ice bath, stirring periodically. The ice cream may then be churned immediately or, if you like, the following day (keep the mixture chilled in the refrigerator until then). The longer the custard cures, the better.
While the custard is cooling in the ice bath and/or curing, make the blueberry "filling" and "topping." In a small sauce pan over medium heat, stir together blueberries, apple juice, and sugar until the sugar is dissolved.
Bring to a boil then lower heat and simmer for about 10-15 minutes, or until the sauce has thickened. Stir in the vanilla.
Allow the compote to cool completely in the refridgerator before using. Again, this can be done in advance, just store in the refridgerator in an airtight container.
Preheat the oven to 350 degrees F. Butter a small baking dish (about 3x6 inches). Combine flour, sugar and butter using a pastry blender, two forks, or a food processor, and mix until it looks like course crumbs. Add oats and cinnamon and mix a little more. Spread topping evenly in buttered dish, and pat down gently with your fingertips. Bake until the top is light brown and crisp, about 25 minutes. Let it cool completely, then break into 1 inch pieces.
Pour the custard into the chilled bowl of your ice cream maker and churn for about 25-30 minutes. At the end, swirl in the blueberry filling and churn some more. Do the same with the chunks of crisp. Freeze in an airtight container in the freezer at least 1 hour before enjoying.
Notes
Ice cream base based on Tyler Florence's Vanilla Ice Cream Base, via Food Network.