Frozen Strawberry Custard with Lemon Curd Swirl

Working in batches, pulse the strawberries in a food processor until finely chopped but not pureed. Scrape the strawberries into a large bowl and stir in the lemon juice and 1/4 cup of the sugar. Let stand at room temperature for 1 hour.

Meanwhile, in a large saucepan, combine the heavy cream and milk and bring just to a simmer. In a large bowl, using a handheld mixer, beat the eggs at medium speed until frothy. Add the vanilla, salt and the remaining 3/4 cup of sugar. Beat at high speed until thick and pale, about 5 minutes. With the machine on, very gradually whisk in 1 cup of the hot cream mixture, then whisk in the rest. Scrape the mixture back into the saucepan and cook over moderately low heat, stirring constantly with a rubber spatula, until thickened, about 15 minutes. (The custard should be thick enough to coat the back of the spatula.)

Strain the custard through a fine mesh sieve into a large stainless-steel bowl set in an ice water bath. Let stand, stirring occasionally, until well chilled, about 20 minutes. Stir in the strawberries with their juices, then refrigerate until cold, about 1 hour.

In two batches, freeze the custard in an ice cream maker according to the manufacturer's instructions; when the custard is thick but not firm, scrape it into a medium bowl and using a rubber spatula, gently fold in 1/2 cup of the lemon curd per batch. Freeze the strawberry custard in airtight containers until firm, about 2 hours.