Directions

1. Prep for the lemon syrup: Using a vegetable peeler, remove the zest from 2 of the lemons in large strips; reserve. Halve the lemons and squeeze enough juice to make 1/2 cup. Combine the lemon juice and sugar in a saucepan and bring to a simmer over medium heat, stirring until the sugar is dissolved. Remove from the heat and refrigerate until chilled. This won't be a very thick syrup.
2. Prep for the ice cream base: 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.
3. Cook: Combine the remaining milk, the cream, sugar, corn syrup, and lemon zest in a 4-quart saucepan, bring to a rolling boil over medium-high heat, and boil for 4 minutes—watch it closely and stir occasionally to make sure it doesn't boil over. 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 heatproof spatula, until slightly thickened, about 1 minute. Remove from the heat.
4. Chill: Gradually whisk the hot milk mixture into the cream cheese until smooth. Pour the mixture into a 1-gallon Ziploc freezer bag and submerge the sealed bag in the ice bath. Let stand, adding more ice as necessary, until cold, about 30 minutes.
5. Freeze: Remove the lemon zest. Pour the ice cream base into the frozen canister and turn on the machine. Pour the lemon syrup through the opening in the top of the machine, and continue to spin the ice cream until thick and creamy.
6. Pack the ice cream into a storage container, press a sheet of parchment directly against the surface, and seal with an airtight lid. Freeze in the coldest part of your freezer until firm, about 4 hours.