In a medium saucepan, heat cream, basil leaves, and lemon zest over medium-low heat until it is beginning to bubble around the edges of the pan and is hot to the touch. When hot and bubbly, remove from the heat and cover. Let steep for 30 minutes, then strain out basil and lemon zest.
Return the steeped cream to the medium saucepan and set it back over the heat. Bring the cream back to a simmer. While the cream is heating, whisk together sugar, egg yolks, salt, and vanilla extract until a thick paste forms. When the cream is hot, slowly stream it into the egg mixture. Transfer the entire mixture back into the saucepan and return to heat.
Cook, stirring continually with a wooden spoon, over low-medium heat until the sauce is thickened, but do not bring to a boil. When the sauce is sufficiently thickened, remove from heat and immediately strain into a large mixing bowl. Press a piece of plastic wrap directly over the top of the custard, cover and refrigerate, until completely cold (preferably overnight).
When the ice cream base is cold, transfer it to the bowl of a stand mixer fitted with the whisk attachment. Whip on medium-high speed until soft peaks form and then, with the mixer running, stream in the 1/4 cup of Monini Basil Extra Virgin Olive Oil. Spread the whipped cream mixture into a 8×8” loaf pan, press a piece of plastic wrap directly on the surface, wrap tightly, and freeze for at least 12 hours. To serve, scoop ice cream and drizzle with more olive oil.