In a small heavy-bottomed saucepan, combine the fresh blueberries, 1/4 cup granulated sugar, lemon juice, and water. Bring the mixture to a simmer over medium heat, stirring occasionally.

Continue to simmer for 8-10 minutes, or until the blueberries have softened and burst, and the sauce has thickened slightly. Mash some of the blueberries with a fork or potato masher for a chunkier compote, or blend briefly with an immersion blender for a smoother consistency. Remove from heat and let cool completely. For best results, chill in the refrigerator while preparing the ice cream base.

In a medium heavy-bottomed saucepan, combine the whole milk, heavy cream, and 3/4 cup granulated sugar. Heat over medium heat, stirring occasionally, until the sugar dissolves and the mixture just begins to simmer around the edges (do not boil). Remove from heat.

In a separate medium bowl, whisk the egg yolks until light and creamy. Slowly temper the egg yolks by gradually whisking about 1/2 cup of the hot milk mixture into the yolks. This prevents the yolks from scrambling.

Pour the tempered yolk mixture back into the saucepan with the remaining hot milk mixture. Return the saucepan to low-medium heat and cook, stirring constantly with a rubber spatula, until the mixture thickens enough to coat the back of the spoon (it should reach about 175-180°F or 80-82°C). Do not boil or the custard may curdle.

Remove the custard from the heat. Pour it through a fine-mesh sieve into a clean bowl to remove any potential bits of cooked egg. Stir in the vanilla extract and pinch of salt. Cover the bowl with plastic wrap, pressing it directly onto the surface of the custard to prevent a skin from forming. Chill the custard thoroughly in the refrigerator for at least 4 hours, or preferably overnight, until it is very cold.

Once the custard base is thoroughly chilled, pour it into your ice cream maker and churn according to the manufacturer's instructions, usually for 20-25 minutes, until it reaches the consistency of soft-serve ice cream.

During the last 5 minutes of churning, or immediately after churning, gently swirl in the chilled blueberry compote. Do not overmix if you want distinct streaks of blueberry.

Transfer the churned ice cream to an airtight freezer-safe container. Press plastic wrap directly onto the surface of the ice cream, then cover with a lid. Freeze for at least 2-4 hours, or until firm, before serving.