Using a vegetable peeler, remove the zest from 2 lemons. You’ll want large strips of zest, with no white pith.
In a medium heavy bottom saucepan, combine the lemon zest and sugar with 2 cups of milk, sea salt and corn syrup. Bring the mixture to a boil over medium-high heat and cook for 3 minutes stirring frequently. Remove from the heat and cover with a lid. Steep for 30 minutes.
Combine the cornstarch with the remaining 2 tablespoons of milk. Stir until smooth and set aside.
Set the saucepan back on the stove top and warm on medium-high. Whisk in the cornstarch slurry and cook until slightly thickened, about 1 minute.
Remove from the heat and whisk in the cream cheese adding one piece at a time. Whisk until melted then add lemon juice. Whisk until blended.
Set a large clean bowl in an ice bath. Add the heavy cream to the clean bowl and place a fine mesh sieve over the bowl. Pour the warm ice cream base through the sieve into the bowl with the heavy cream. Discard lemon zest. Whisk the ice cream every five minutes or so, or until cooled, about 30 minutes.
Cover and refrigerate for 8 hours or overnight. Process according to the manufacturer’s directions for your ice cream maker.
Spoon about ⅓ of the lemon ice cream into an airtight container. Dollop ⅓ of the lemon curd in spoonfuls on top. Repeat with half the remaining ice cream and half of the remaining curd. Make a third layer, using all the ice cream base and curd. Swirl the curd into the ice cream using a table knife. Cover and freeze until set. This can take up to 8 hours for the best consistency.
Base ice cream adapted Jeni’s Splendid Ice Creams at Home cookbook