Bring a medium size pot of water to a boil. Add basil leaves and cook for 30 seconds. Quickly drain basil and rinse with cold water to stop cooking process.
Wring as much water as you can out of the basil by squeezing it in your hand, then wrap basil in several thickness of paper towels and squeeze again.
Add basil, lemon zest and sunflower oil to a blender container and blend for 1 minute until mixture is finely pureed.
Pour mixture into a small saucepan and add olive oil. Heat on medium high heat for 1-2 minutes, just until mixture begins to bubble slightly at the edges. Do not boil!
Pour mixture through a fine-mesh strainer (the finer, the better) into a jar or storage container.
Store in refrigerator for 1-2 weeks or freeze in small containers for 3-4 months.