How to Make It
Stir together sugar, powdered milk, and xanthan gum in a small bowl. Whisk together milk and corn syrup in a medium saucepan. Add sugar mixture, and whisk until smooth. Heat mixture over medium, whisking often, until sugar has fully dissolved, 3 to 4 minutes. (Do not simmer.) Remove from heat, and whisk in cream. Cover and chill at least 6 hours. For even better texture and flavor, chill mixture up to 24 hours. Base can be stored in an airtight container in freezer for up to 3 months; thaw completely before using.
Whisk together chilled base, olive oil, and kosher salt until well combined. (There will still be little droplets of oil on the surface.) Pour mixture into freezer bowl of a 11/2-quart electric ice cream maker, and proceed according to manufacturer’s directions until ice cream has the texture of soft-serve, about 35 minutes. (Instructions and times may vary.)
Quickly transfer ice cream to a freezer-safe container; press parchment paper directly onto surface. Cover container, and freeze until firm, at least 6 hours. Ice cream can be stored in freezer up to 3 months. To serve, garnish with olive oil and flaky sea salt.
Xanthan gum can be found by the specialty flours or near the baking powder in grocery stores.