Preheat oven to 375 degrees F. Combine strawberries with sugar in an 8" square glass or ceramic baking dish, stirring gently to mix well. Roast for 8 minutes, or until just soft. Let cool slightly. Puree in a food processor with lemon juice. Measure 1 cup of the pureed berries; refrigerate the rest of the puree for another use.

Mix about 2 tablespoons of the milk with the cornstarch in a small bowl to make a smooth slurry. Whisk the cream cheese and salt in a medium bowl until smooth. Fill a large bowl with ice and water.

Combine the remaining milk, cream, sugar and corn syrup in a 4-quart saucepan, bring to a rolling boil over medium-high heat, and boil for 4 minutes. Remove from the heat and gradually whisk in the cornstarch slurry. Bring the mixture back to a boil over medium-high heat and cook, stirring with a heat-proof spatula, until slightly thickened, about 1 minute. Remove from heat.