Combine sugar and basil leaves in a food processor or blender and mix until well-combined.

Add basil sugar to a small stock pot with cream, milk, olive oil, salt, and lemon juice.

Cook over medium-high heat until bubbly and hot. In the meantime, bloom gelatin sheets in a bowl of cold water.

Remove scalding milk mixture from heat and add the bloomed gelatin. Blend mixture carefully with an immersion blender until basil is fully incorporated.

Strain mixture into a large pyrex measuring cup, removing any basil sediment. Let cool slightly.

Place silicon dome molds on a baking sheet in your fridge. Carefully pour the panna cotta liquid into each dome mold.

Let domes cool for 1-2 hours, then cover with plastic wrap. Let chill overnight, or up to 2 days.