Mix the heavy cream, milk, sugar, zest, salt and vanilla in a medium pot over the stove. Warm over medium-high heat until you see bubbles on the surface, approximately 9 minutes. Whisk occasionally. Remove from the heat as soon as you see it boil.

Steadily and slowly pour the olive oil into the cream mixture, whisking constantly.

Stir in the lemon juice. I highly recommend blending in a high speed blender for the most luscious texture and flavor. Cool the mixture in the fridge or use an ice bath to save time.

Pour the chilled lemon mixture into the freezer bowl of a 1 1/2-quart electric ice cream maker, and proceed according to manufacturer's instructions.

Transfer ice cream to a freezer-safe container; press a sheet of parchment paper or plastic wrap directly on the surface, and seal with an airtight lid. Place in the freezer for at least 4 hours or overnight.