Preparation

Make the syrup:

• In a 2-quart heavy-based saucepan, combine the berries, corn syrup, lemon juice, and cinnamon. Set the pan over low heat and mash the berries roughly with a potato masher or the back of a large fork. Increase the heat to medium low and bring the mixture to a simmer. Simmer for 5 minutes, stirring occasionally, and then let cool for 5 to 10 min.
• Put the berries in a fine sieve set over a bowl. Press on the berries to extract all the liquid; discard the solids. You’ll have about 1 cup liquid.
• In a separate bowl, beat the egg white just enough to loosen and break it up, but try to incorporate as little air as possible. Stir the beaten white into the blueberry syrup just until well combined, cover with plastic wrap, and refrigerate until thoroughly chilled. You can make the syrup up to three days ahead of making the ice cream.

Make the custard:

• In a 1- to 2-quart heavy-based saucepan, heat the half-and-half over medium heat. Bring just to a boil, watching so it doesn’t boil over, and then remove it from the heat.
• Meanwhile, in a medium bowl, lightly beat the yolks to break them up. Whisk in the sugar just until incorporated. Don’t overwhisk; you don’t want a very thick, pale mixture. Set the bowl on a damp towel to hold it steady and very slowly pour the hot half-and-half over the egg mixture, whisking constantly so the yolks don’t curdle. Rinse the saucepan but don’t dry the inside; a film of water helps prevent the custard from sticking to the pot. Have ready a fine sieve set over a bowl. Return the custard to the saucepan and set it over medium-low heat. Stirring constantly with a wooden spoon, cook the custard until it thickens enough to coat the back of the spoon, 7 to 10 min.; a finger drawn across the back of the spoon should leave a clean trail. Immediately pour the custard through the sieve. Stir in the cream and the vanilla extract and press a piece of plastic onto the surface of the warm custard to keep a skin from forming. Poke a few slits in the plastic with the tip of a paring knife to let the steam escape. Let cool slightly and then refrigerate until well chilled, at least 4 hours but ideally 8 hours or overnight.

Make the ice cream:

• Stir the blueberry syrup into the chilled custard; mix thoroughly. Pour the mixture into an ice-cream maker and freeze following the manufacturer’s instructions. For the most intense flavor, serve right away. Otherwise, store in an airtight container for up to a week; let the ice cream soften in the refrigerator for 10 minutes before serving to coax out more flavor.