Start the vanilla ice cream: In a medium saucepan, warm the milk, 1 cup of cream, 3/4 cup sugar, and salt over medium heat. Stir to dissolve the sugar. When the milk starts to steam, turn off the heat. Using the tip of a paring knife, scrape the seeds from the vanilla bean pod. Place the seeds and the whole pod into the heated milk. Cover with a tight-fitting lid and let steep for 30 minutes.
Roast the strawberries: Oven 300°F. If the strawberries are large, cut them in half. Place the strawberries in a medium bowl and toss with sugar. Line a rimmed baking sheet with a silpat mat. Pour the strawberries into the center of the baking sheet. Roast for 30-45 minutes until the juices start running from the strawberries and the berries look slightly mushy. Remove from oven and scrape everything (juices and caramelized sugar) into the same medium bowl. Mash the berries with a fork or a potato masher. Stir in the corn syrup. Set aside.
Make the ice cream: Warm the milk mixture up over medium heat until steaming. Place the yolks in a medium bowl and break them up with a whisk. Whisk in a half cup of the warm milk mixture until blended. Whisk in another half cup of the warm milk. Scrape the egg mixture back into the pan with the rest of the milk mixture, whisking to incorporate. Set the pan over medium heat and stir constantly, making sure to get the corners of the pan, until the custard thickens and can coat the back of a spoon. Strain the custard through a fine mesh sieve into a large bowl. Add the remaining cup of heavy cream. Stir in the vanilla extract and the roasted strawberry mash. Chill the custard in the refrigerator (covered) or over an ice bath. When the custard is completely chilled, remove the vanilla bean pod and churn the custard in your ice cream machine according to the manufacturer’s directions.