Start by mashing the raspberries in a bowl with 1/4 cup of the sugar until they break down but still have some texture. Set aside to let the sugar draw out the juices while you make the base.
In a medium saucepan, combine the heavy cream, milk, remaining 1/2 cup sugar, and salt. Heat over medium, stirring occasionally to dissolve the sugar.
While the cream mixture heats, whisk the egg yolks in a medium bowl until they lighten in color slightly, about 30 seconds. This makes them easier to temper.
Once you see tiny bubbles around the edges of the cream mixture, remove it from the heat. Slowly ladle about 1 cup of the hot cream mixture into the egg yolks, whisking constantly. This gradual warming prevents the eggs from scrambling.
Pour the warmed egg mixture back into the saucepan, whisking constantly. Return to medium-low heat and cook, stirring continuously with a wooden spoon or silicone spatula. Make sure to scrape the bottom and sides of the pan as you stir.
The custard is ready when it thickens enough to coat the back of your spoon and hold a line when you run your finger through it – this usually takes 5-7 minutes.
Strain the custard through a fine-mesh sieve into a clean bowl. Stir in the vanilla extract and corn syrup until fully incorporated. Press plastic wrap directly onto the surface (this prevents a skin from forming) and refrigerate until completely cold, at least 4 hours or overnight.
While the base chills, roughly chop your chocolate. The varying sizes create nice texture throughout the ice cream.
When you’re ready to churn, stir the cold custard base to recombine everything. Pour into your ice cream maker and churn according to the manufacturer’s instructions.
In the last minute of churning, add the reserved raspberry mixture. The ice cream should be thick but still soft-serve consistency.
Layer about one-third of the ice cream into your storage container, sprinkle with some chocolate chunks. Repeat twice more with remaining ice cream and chocolate, ending with chocolate on top.
Press a piece of wax paper or parchment directly on the surface, cover, and freeze until firm, at least 4 hours. The ice cream will keep for about 2 weeks, but the texture is best in the first few days.