Preparation

• In a 4-quart saucepan, bring 2 inches of water to a boil over high heat. Reduce the heat to a simmer. In a stainless-steel bowl that fits over the saucepan without touching the water, combine the sugar, lemon juice, eggs, egg yolk, butter, lemon extract, and salt. Whisk vigorously until the mixture thickens to the consistency of pudding, 7 to 8 minutes.
• Remove the bowl from the saucepan and whisk in the cream and milk. Strain through a fine-mesh sieve into a medium bowl and refrigerate until thoroughly chilled, at least 4 hours or up to 1 day, covering with plastic wrap once cool.
• Stir the lemon mixture and churn it in an ice cream machine according to the manufacturer’s instructions until it’s the consistency of soft-serve ice cream. Serve or pack into a container, seal, and store in the freezer for up to 1 week.