Bring milk and cream to a boil in a medium saucepan.
Meanwhile, in a medium bowl, whisk the yolks and sugar together until very well blended and just slightly thickened.
Still whisking, drizzle in about 1/3 of the hot liquid—this will temper, or warm, the yolks so they don’t curdle.
Whisking all the while, slowly pour in the remaining liquid.
Pour the custard back into the pan and cook over medium heat, stirring without stopping, until the custard thickens slightly and coats the back of a spoon; if you run your finger down the bowl of the spoon, the custard should not run into the track.
The custard should reach at least 170°, but no more than 180°, on an instant read thermometer.
Immediately remove pan from the heat and pour the custard over the chopped chocolate.
Let the mixture sit for 1 minute, then using a rubber spatula, starting in the center of the measuring cup and working in ever-wider concentric circles, stir until the custard is smooth.
Refrigerate the custard until chilled before churning it into ice cream.
Scrape the chilled custard into the bowl of an ice cream maker; churn according to manufacturer’s directions.
When the ice cream is thickened and just about ready, spoon in the blueberry preserves and churn to blend.
Pack the ice cream into a container and freeze it until it is firm enough to scoop.