Combine the chilled heavy cream in a blender or food processor and blend until it becomes slightly thickened and soft peaks form.
Add the sweetened condensed milk, lemon zest, lemon juice, and chopped basil leaves to the whipped cream.
Blend everything together for about 30 seconds until smooth and well combined, with basil evenly incorporated.
Pour the mixture into a freezer-safe container, smoothing the top with a spatula for an even surface.
Cover the container with a lid or plastic wrap and place it in the freezer.
Freeze for at least 4 hours or until the ice cream is firm and scoopable.
Remove the ice cream from the freezer, scoop into bowls, and serve immediately to enjoy the creamy, bright flavors.