Rosemary Ice Cream with Olive Oil

0 Infuse the Milk: In a saucepan, combine the milk, lemon zest (or skip if using extract later), and rosemary sprigs. Stir in milk powder (if using). Warm over medium heat until steaming but not boiling, about [timer minutes=3]3 minutes[/timer]. Reduce heat to low, cover, and gently simmer for [timer minutes=4]4 minutes[/timer]. Remove from heat and strain out the zest and rosemary.
1 Make the Custard Base: Return 1½ cups of the infused milk to the saucepan and heat over medium heat. Whisk in the honey and salt. In a separate bowl or measuring cup, whisk the remaining ¾ cup milk with the cornstarch until completely smooth with no lumps.
2 Once the milk mixture is hot, slowly whisk in the cornstarch slurry, stirring constantly. Cook over medium heat, stirring continuously, until thickened and gently bubbling, about 180 to 190°F (82 to 88°C). Continue cooking for [timer minutes=1]1 to 2 minutes[/timer] to fully cook out the starch flavor. Remove from heat.
4 Add the Cream and Olive Oil: Stir in the chilled heavy cream. Let the mixture cool slightly to about 110 to 120°F (43 to 49°C). Add olive oil and using an immersion blender, blend it in until the base looks smooth and glossy. Add the lemon juice, extra honey (if using) and blend again using quick, short pulses on low speed. (If using lemon extract instead of zest, add it now.)
5 Chill and Churn: Cover and chill the base thoroughly, preferably overnight. Churn in your ice cream maker according to the manufacturer’s instructions. Enjoy immediately for a soft-serve texture, or freeze until firm.