Combine the berries and ¼ cup sugar in a small pot. Stir to combine and place the pot over low heat. The heat and sugar will help to encourage the berries to release their juices.
Separate the eggs, placing the yolks in a medium bowl. Whisk them briskly until they thicken slightly. Reserve the whites for another use.
In a medium saucepan, combine the egg yolks, heavy cream, ¾ cup granulated sugar, and salt. Place the pan over low heat, stirring frequently to encourage the sugar to fully dissolve into the liquid.
Whisk as the mixture warms to keep the custard from scorching as it cooks. The custard will thicken as it comes to a bare simmer, coming to a pudding like consistency when finished. The properly thickened custard will coat the back of a spoon.
Remove the pan from the heat. Place a fine mesh strainer or colander lined with cheesecloth over a large bowl. Transfer the warm custard to the strainer and allow it to pass through to the bowl beneath. This will ensure that the custard is completely smooth and does not contain any undissolved grains of sugar or cooked egg. Continue until all of the custard has been strained.
Transfer the warm berry mixture to the strainer, pressing the berries against the strainer to release all of their juices into the bowl. Add the whipping cream and vanilla extract to the bowl. Whisk to combine all of the ingredients.
Chill the ice cream base until it is completely cooled. Attempting to churn ice cream or custard before the mixture is completely chilled will result in an unpleasant grainy texture. If you can, allow the custard to cool overnight in the refrigerator. You can also place the bowl of custard inside a larger bowl filled with ice water to hasten the cooling by several hours.
After the base has cooled completely, process it in your ice cream freezer according to the manufacturer’s directions. As the ice cream churns, melt the chocolate in a small bowl either by microwaving in 30 second intervals or by using a double boiler. Allow the chocolate to cool to room temperature as the ice cream processes.
When the ice cream is nearly finished and has taken on a somewhat solid state, add the chocolate. Drizzle the melted chocolate into the ice cream machine while it is running. The chocolate will solidify and then break into lovely bite size bits with the movement of the machine. Remove the ice cream from the machine and place it in a freezer safe container. Freeze until firm and enjoy every single bite!